{"id":10698,"date":"2021-02-10T19:40:16","date_gmt":"2021-02-10T14:10:16","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/ol\/?p=10698"},"modified":"2021-05-26T10:54:23","modified_gmt":"2021-05-26T05:24:23","slug":"circle-ii","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/ol\/ordinary-level\/circle-ii\/","title":{"rendered":"\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba II"},"content":{"rendered":"\n
\n
\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n

\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dad\u0dca \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0dba\u0dcf \u0d9a\u0dbb\u0db1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0da7 \u0dbd\u0db8\u0dca\u0db7 \u0dc0\u0dda.<\/span><\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda AB \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba C \u0dc0\u0dda. OC \u0dc4\u0dcf  AB \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0dc0\u0dda. \u0d91\u0dc0\u0dd2\u0da7 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dc4\u0dd2 O\\widehat{C}<\/span>A = O\\widehat{C}<\/span>B  = 90\u00b0 \u0dc0\u0dda.<\/p>\n\n\n\n

\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab<\/strong> –<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u0db8\u0dd9\u0db8 \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0daf\u0dad\u0dca\u0dad \u0d87\u0dbb\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca \u0db4\u0dc4\u0dad \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1\u0dc0\u0dbd\u0da7 \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb\u0dd4 \u0dc3\u0db4\u0dba\u0db1\u0dca\u0db1. A \u0dba\u0db1\u0dd4 \u0dc0\u0dd8\u0dad\u0dca\u0dad \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0daf Q \u0dba\u0db1\u0dd4 PR \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba \u0daf \u0dc0\u0dda.  PR = 8cm \u0d9a\u0dd2. <\/strong><\/p>\n\n\n\n

I) AQR \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

II) PQ \u0dc4\u0dcf RQ \u0dc4\u0dd2 \u0daf\u0dd2\u0d9c \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

III) \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dd3 \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab \u0db1\u0db8\u0dca \u0d9a\u0dbb\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

IV) \u0d89\u0dc4\u0dad \u0d91\u0d9a\u0dca \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0da7 \u0db4\u0ddb\u0dad\u0d9c\u0dbb\u0dc3\u0dca \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dba\u0ddc\u0daf\u0db1\u0dca\u0db1. \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb\u0dd4<\/strong><\/p>\n\n\n\n

I)90\u00b0 (\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dad\u0dca \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0dba\u0dcf \u0d9a\u0dbb\u0db1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0da7 \u0dbd\u0db8\u0dca\u0db7 \u0dc0\u0dda.)<\/span><\/p>\n\n\n\n

II) PQ = 4cm , QR = 4cm         <\/p>\n\n\n\n

III) APQ, ARQ<\/p>\n\n\n\n

IV) ARQ \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0da7 \u0db4\u0ddb\u0dad\u0d9c\u0dbb\u0dc3\u0dca \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dba\u0dd9\u0daf\u0dd3\u0db8\u0dd9\u0db1\u0dca,<\/p>\n\n\n\n

            AR2<\/sup> = AQ2<\/sup> + RQ2<\/sup><\/p>\n\n\n\n

            AR = 32<\/sup> +  42<\/sup><\/p>\n\n\n\n

                   = 9 + 16<\/p>\n\n\n\n

                   = 25<\/p>\n\n\n\n

            AR = \u221a25<\/p>\n\n\n\n

                    = 5cm<\/p>\n\n\n\n

   \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba = 5cm<\/p>\n\n\n\n

\u0d85\u0db7\u0dca\u200d\u0dba\u0dcf\u0dc3<\/strong><\/strong><\/p>\n\n\n\n

1.<\/strong> \u0dbb\u0dd6\u0db4\u0dba\u0dda O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda AB \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba M \u0dc0\u0dda.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

I) AB,OM \u0dbb\u0dda\u0d9b\u0dcf \u0d85\u0dad\u0dbb \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

II) OMB \u0d9a\u0ddd\u0dab\u0dba \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

III) \u0dc3\u0dd8\u0da2\u0dd4\u0d9a\u0ddd\u0dab\u0dd2\u0d9a \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0db1\u0db8\u0dca \u0d9a\u0dbb\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

IV) AMO \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0dda \u0db4\u0dcf\u0daf \u0d85\u0dad\u0dbb \u0db4\u0dc4\u0dad \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dad\u0dc0\u0dba\u0da7 \u0d9c\u0dd0\u0dbd\u0db4\u0dd9\u0db1 \u0dc3\u0dda \u0dc4\u0dd2\u0dc3\u0dca\u0dad\u0dd0\u0db1\u0dca \u0db4\u0dd4\u0dbb\u0dc0\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

AO2<\/sup> = OM2 <\/sup>+ \u2026..<\/p>\n\n\n\n

2. <\/strong>\u0db4\u0dc4\u0dad \u0dbb\u0dd6\u0db4 \u0dc3\u0da7\u0dc4\u0db1\u0dca\u0dc0\u0dbd \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dad\u0ddc\u0dbb\u0dad\u0dd4\u0dbb\u0dd4 \u0d87\u0dc3\u0dd4\u0dbb\u0dd9\u0db1\u0dca<\/p>\n\n\n\n

a) \u0d91\u0d9a\u0dca \u0d91\u0d9a\u0dca \u0dbb\u0dd6\u0db4 \u0dc3\u0da7\u0dc4\u0db1 \u0dc3\u0db3\u0dc4\u0dcf \u0db4\u0ddb\u0dad\u0d9c\u0dbb\u0dc3\u0dca \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dba \u0dba\u0ddc\u0daf\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

b) \u0d91\u0db8 \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dad\u0dcf\u0dc0 \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0d9a\u0dbb x \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1. ( C \u0dba\u0db1\u0dd4 \u0dc0\u0dd8\u0dad\u0dca\u0dad \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dba\u0dd2.)<\/p>\n\n\n\n

I)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

II)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

III)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

IV)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

3. <\/strong>\u0d85\u0dbb\u0dba 10cm \u0dc0\u0db1 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dd9\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dda \u0dc3\u0dd2\u0dba \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dca\u200d\u0dba\u0dba\u0da7 \u0d87\u0db3\u0dd2 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0\u0dda \u0daf\u0dd2\u0d9c 6cm \u0d9a\u0dd2.<\/p>\n\n\n\n

I) \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0daf\u0dad\u0dca\u0dad \u0dc0\u0dbd\u0da7 \u0d9c\u0dd0\u0dbd\u0db4\u0dd9\u0db1 \u0dbb\u0dd6\u0db4 \u0dc3\u0da7\u0dc4\u0db1\u0d9a\u0dca \u0d85\u0db3\u0dd2\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

II) \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.  <\/p>\n\n\n\n

4.<\/strong> \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dca\u0dad\u0dda O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a AC \u0dc0\u0dd2\u0dc1\u0dca\u0d9a\u0db8\u0dca\u0db7\u0dba \u0dc0\u0dd6 ABC \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2. \u0d91\u0dc4\u0dd2 AB,BC \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0db1\u0dca \u0db4\u0dd2\u0dc5\u0dd2\u0dc0\u0dd9\u0dbd\u0dd2\u0db1\u0dca 6cm,8cm \u0dc0\u0dda.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

I) OEB \u0d9a\u0ddd\u0dab\u0dba \u0dc4\u0dcf ODB \u0d9a\u0ddd\u0dab\u0dba \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

II) EOD \u0d9a\u0ddd\u0dab\u0dba \u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

III) BE \u0daf\u0dd2\u0d9c \u0d9a\u0dd3\u0dba \u0daf?<\/p>\n\n\n\n

IV) BD \u0daf\u0dd2\u0d9c \u0d9a\u0dd3\u0dba \u0daf?<\/p>\n\n\n\n

V) ODBE \u0da0\u0dad\u0dd4\u0dbb\u0dc3\u0dca\u200d\u0dbb\u0dba\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

5.<\/strong> \u0db4\u0dc4\u0dad \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dd2 O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dc0\u0dbd \u0dc0\u0dd3\u0da2\u0dd3\u0dba \u0dc3\u0d82\u0d9a\u0dda\u0dad \u0db8\u0d9c\u0dd2\u0db1\u0dca \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dd2 \u0d9a\u0ddd\u0dab\u0dc0\u0dbd \u0d85\u0d9c\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

I)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

II)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

III)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u0db4\u0dd2\u0dbd\u0dd2\u0dad\u0dd4\u0dbb\u0dd4<\/strong><\/strong><\/p>\n\n\n\n

1.<\/strong><\/p>\n\n\n\n

I) AB \u0dc4\u0dcf OM \u0dbd\u0db8\u0dca\u0db7\u0d9a\u0dba. (\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dad\u0dca \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0dba\u0dcf \u0d9a\u0dbb\u0db1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0da7 \u0dbd\u0db8\u0dca\u0db7 \u0dc0\u0dda.)<\/span><\/p>\n\n\n\n

II) 90\u00b0<\/p>\n\n\n\n

III) AOM , BOM<\/p>\n\n\n\n

IV) AO2<\/sup> = OM2 <\/sup>+ AM2<\/sup><\/p>\n\n\n\n

2.<\/strong>
I) a) x2 <\/sup>+ 42<\/sup> = 52<\/sup>       
b) x2<\/sup> + 16 = 25                      
x2<\/sup> = 25-16                       
x2<\/sup> = 9                         
x = \u221a9                         
x = 3cm  <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
II) 
a)  x2 <\/sup>+ 62<\/sup> = 102<\/sup>       
b) x2<\/sup> + 36 = 100                       
x2<\/sup> = 100-36                        
x2<\/sup> = 64                         
x = \u221a64                         
x = 8cm  <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
III) 
a) x2   <\/sup>= 52 <\/sup>+ 122<\/sup>           
b) x2<\/sup> = 25+144                        
x2<\/sup> = 169                         
x = \u221a169                         
x = 13cm  <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
IV )
a) x2 <\/sup>+ 122<\/sup> = 152<\/sup>       
b) x2<\/sup> + 144 = 225                       
x2<\/sup> = 225-144                        
x2<\/sup> = 81                         
x = \u221a81                         
x = 9cm  <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

3.<\/strong><\/p>\n\n\n\n

I)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

II)<\/p>\n\n\n\n

62 <\/sup>+ BC2 <\/sup>= 102<\/sup><\/p>\n\n\n\n

36 + BC2<\/sup> = 100<\/p>\n\n\n\n

BC2 <\/sup>= 100-36<\/p>\n\n\n\n

BC2<\/sup> = 64<\/p>\n\n\n\n

BC = \u221a64<\/p>\n\n\n\n

BC = 8 cm<\/p>\n\n\n\n

\u0da2\u0dca\u200d\u0dba\u0dcf\u0dba = AC = 2BC<\/p>\n\n\n\n

\u0da2\u0dca\u200d\u0dba\u0dcf\u0dba = 2 \u00d7 8<\/p>\n\n\n\n

= 16cm<\/p>\n\n\n\n

4. <\/strong>      <\/p>\n\n\n\n

I) 90\u00b0<\/p>\n\n\n\n

 II) 90\u00b0<\/p>\n\n\n\n

III) BE = 4cm<\/p>\n\n\n\n

IV)  BC = 3cm<\/p>\n\n\n\n

V) ODBE \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba = 14cm<\/p>\n\n\n\n

5.  <\/strong>
I)
O\\widehat{B}<\/span>C = 90\u00b0  
x + 90\u00b0 + 30\u00b0 = 180\u00b0
          x + 120\u00b0 = 180\u00b0
                      x = 180\u00b0- 120\u00b0
                       x = 60\u00b0

II) O\\widehat{B }<\/span>A = 90\u00b0                      
O\\widehat{A}<\/span>B = A\\widehat{O}<\/span>B (\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0db4\u0dcf\u0daf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0db8\u0dcf\u0db1 \u0db1\u0db8\u0dca \u0d92 \u0db4\u0dcf\u0daf\u0dc0\u0dbd\u0da7 \u0dc3\u0db8\u0dca\u0db8\u0dd4\u0d9b \u0d9a\u0ddd\u0dab \u0daf \u0dc3\u0db8\u0dcf\u0db1 \u0dc0\u0dda.)<\/strong>           <\/span>
x+ x + 90\u00b0 = 180\u00b0             
2x + 90\u00b0 = 180\u00b0                         
2x = 180\u00b0- 90\u00b0                         
2x = 90\u00b0                          
x = 45\u00b0               <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
III)
O\\widehat{B}<\/span>A= 90\u00b0
y + 90\u00b0 + 20\u00b0 = 180\u00b0          
y + 110\u00b0 = 180\u00b0                       
y = 180\u00b0- 110\u00b0                       
y = 70\u00b0 , B\\widehat{A}<\/span>D = z \u0dbd\u0dd9\u0dc3 \u0d9c\u0db1\u0dd2\u0db8\u0dd4            
20 + z =x (OA = OD, \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a \u0db4\u0dcf\u0daf \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dc3\u0db8\u0dcf\u0db1 \u0db1\u0db8\u0dca \u0d92 \u0db4\u0dcf\u0daf\u0dc0\u0dbd\u0da7 \u0dc3\u0db8\u0dca\u0db8\u0dd4\u0d9b \u0d9a\u0ddd\u0dab \u0daf \u0dc3\u0db8\u0dcf\u0db1 \u0dc0\u0dda.<\/strong>)    <\/span>      
z = x – 20\u00b0   
AOD \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0dda
70\u00b0+20\u00b0 + z+ x = 180\u00b0
x + z = 90\u00b0                                               
x + x – 20\u00b0 = 90\u00b0
x = 55\u00b0                 <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

                  <\/p>\n\n\n\n

\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0da7 \u0d85\u0db3\u0dd2\u0db1\u0dd4 \u0dbd\u0db6\u0db1 \u0dbd\u0db8\u0dca\u0db6\u0dba\u0dd9\u0db1\u0dca \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba  <\/strong> \u0dc3\u0db8\u0da0\u0dca\u0da1\u0dda\u0daf\u0db1\u0dba \u0dc0\u0dda<\/strong><\/span>.<\/span><\/strong>
<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\"\"<\/figure><\/div>\n\n\n\n

O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda AB \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a\u0dd2. OC \u0dc4\u0dcf AB \u0dbd\u0db8\u0dca\u0db8\u0dca\u0db7\u0d9a \u0dc0\u0dda. \u0db1\u0db8\u0dca AC = BC \u0dc0\u0dda.<\/p>\n\n\n\n

\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0db1 – <\/strong><\/p>\n\n\n\n

O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda AB \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a\u0dd2. OC \u0dc4\u0dcf AB \u0dbd\u0db8\u0dca\u0db7\u0d9a \u0dc0\u0dda.  OC = 6cm, AB = 16 cm \u0daf \u0dc0\u0dda.<\/p>\n\n\n\n

I)BC \u0daf\u0dd2\u0d9c \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1<\/p>\n\n\n\n

II) \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

\u0db4\u0dd2\u0dbd\u0dd2\u0dad\u0dd4\u0dbb\u0dd4<\/strong>
I) BC = AB\/2          
= 8cm
II) OB2<\/sup> = OC2 <\/sup>+ BC2<\/sup>          
= 62<\/sup> + 82<\/sup>          
= 36 + 64           
= 100    
OB = \u221a100   
OB = 10cm  

\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba   = 10cm    <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

1.<\/strong> \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd9\u0db1 P \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0db1 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda CD \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a\u0dd2. E \u0dba\u0db1\u0dd4 P \u0dc3\u0dd2\u0da7 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0da7 \u0d87\u0db3\u0dd2 \u0dbd\u0db8\u0dca\u0db7\u0dba\u0dda \u0d85\u0da9\u0dd2\u0dba\u0dba\u0dd2. DE \u0dc4\u0dcf EC \u0d85\u0dad\u0dbb \u0dc3\u0db8\u0dca\u0db6\u0db1\u0dca\u0db0\u0dad\u0dcf\u0dc0\u0d9a\u0dca \u0d9c\u0ddc\u0da9\u0db1\u0d9c\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

2.<\/strong> \u0d85\u0dbb\u0dba 5cm \u0dc0\u0db1 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dda \u0dc3\u0dd2\u0da7 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a\u0da7 \u0d87\u0db3\u0dd2 \u0dbd\u0db8\u0dca\u0db7\u0dba\u0dda \u0daf\u0dd2\u0d9c 3cm \u0d9a\u0dd2. \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0d9c\u0dab\u0db1\u0dba \u0d9a\u0dbb\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

3.<\/strong> PQR \u0dba\u0db1\u0dd4 O \u0d9a\u0dda\u0db1\u0dca\u0da9\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0dc3\u0db8\u0db4\u0dcf\u0daf \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0d9a\u0dd2. SQ = 8cm \u0db1\u0db8\u0dca \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

4.<\/strong> O \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba \u0dc0\u0dd6 \u0d92\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dd2\u0d9a \u0dc0\u0dd8\u0dad\u0dca\u0dad \u0daf\u0dd9\u0d9a\u0d9a\u0dca \u0dbb\u0dd6\u0db4\u0dba\u0dda \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dda. \u0d9a\u0dd4\u0da9\u0dcf \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba 5cm \u0daf \u0dc0\u0dd2\u0dc1\u0dcf\u0dbd \u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0dda \u0d85\u0dbb\u0dba 13cm \u0dc0\u0dda. AB \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dda \u0daf\u0dd2\u0d9c \u0dc3\u0ddc\u0dba\u0db1\u0dca\u0db1.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb\u0dd4<\/strong><\/strong><\/p>\n\n\n\n

1. <\/strong>DE = EC<\/p>\n\n\n\n

2.<\/strong><\/p>\n\n\n\n

OB2<\/sup> = OC2 <\/sup>+ BC2<\/sup><\/p>\n\n\n\n

52<\/sup> = 32<\/sup> + BC2<\/sup><\/p>\n\n\n\n

BC2<\/sup> = 25 \u2013 9<\/p>\n\n\n\n

BC2<\/sup> = 16<\/p>\n\n\n\n

BC = \u221a16<\/p>\n\n\n\n

BC = 4cm<\/p>\n\n\n\n

\u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dba\u0dda \u0daf\u0dd2\u0d9c = 2BC<\/p>\n\n\n\n

               = 8cm<\/p>\n\n\n\n

3.<\/strong><\/p>\n\n\n\n

SQ = PS = 8cm<\/p>\n\n\n\n

PQ = 2 \u00d7 8<\/p>\n\n\n\n

\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0dda \u0db4\u0dcf\u0daf\u0dba\u0d9a \u0daf\u0dd2\u0d9c = 16cm<\/p>\n\n\n\n

\u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0dba\u0dda \u0db4\u0dbb\u0dd2\u0db8\u0dd2\u0dad\u0dd2\u0dba = 16 + 16 + 16<\/p>\n\n\n\n

                          = 48 cm<\/p>\n\n\n\n

4.<\/strong><\/p>\n\n\n\n

OB2<\/sup> = OC2 <\/sup>+ BC2<\/sup><\/p>\n\n\n\n

132 <\/sup>= 52<\/sup> + BC2<\/sup><\/p>\n\n\n\n

169 = 25 + BC2<\/sup><\/p>\n\n\n\n

BC2 <\/sup>= 169 \u2013 25<\/p>\n\n\n\n

BC2<\/sup> = 144<\/p>\n\n\n\n

BC <\/sup>= \u221a144<\/p>\n\n\n\n

BC <\/sup>= 12 cm<\/p>\n\n\n\n

AB = 2BC<\/p>\n\n\n\n

     = 24 cm<\/p>\n\n\n\n

\u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0dba\u0dda \u0daf\u0dd2\u0d9c = 24 cm<\/p>\n\n\n\n

<\/div>\n\n\n\n
\n
\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n

\u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0dba\u0dda\u0daf\u0dd3 \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0dc0\u0db1\u0dca\u0db1\u0dda \u0db8\u0dd9\u0dad\u0db1\u0da7\u0dba\u0dd2.<\/p>\n\n\n\n

\n
\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\n<\/div>\n\n\n\n
<\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

\u0dc0\u0dd8\u0dad\u0dca\u0dad\u0dba\u0d9a \u0d9a\u0dda\u0db1\u0dca\u0daf\u0dca\u200d\u0dbb\u0dba\u0dad\u0dca \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0d9a \u0db8\u0db0\u0dca\u200d\u0dba \u0dbd\u0d9a\u0dca\u0dc2\u0dba\u0dad\u0dca \u0dba\u0dcf \u0d9a\u0dbb\u0db1 \u0dbb\u0dda\u0d9b\u0dcf\u0dc0 \u0da2\u0dca\u200d\u0dba\u0dcf\u0dba\u0da7 \u0dbd\u0db8\u0dca\u0db7 \u0dc0\u0dda. \u0dba\u0db1 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad\u0dba \u0db4\u0dd0\u0dc4\u0dd0\u0daf\u0dd2\u0dc5\u0dd2 \u0d9a\u0dbb \u0d92 \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0db3\u0dc0 \u0d9c\u0dd0\u0da7\u0dbd\u0dd4 \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8 \u0db8\u0dd9\u0db8 \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0daf\u0dd3 \u0dc3\u0dd2\u0daf\u0dd4\u0d9a\u0dd9\u0dbb\u0dda.<\/p>\n","protected":false},"author":21,"featured_media":11442,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3756,3787,3752,3790,3623],"tags":[3695,3646,3687,3644,3688,2180,3643,3651,3649,3650,3696,3666,3665],"class_list":{"0":"post-10698","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-paper-1","8":"category-mathamatics","9":"category-geometry-grade-10","10":"category-3790","11":"category-ordinary-level","12":"tag-circle","13":"tag-ganithaya","14":"tag-mathamatics","15":"tag-maths","16":"tag-mathz","17":"tag-ol","18":"tag-ordinary-level","19":"tag-saamaanya-pela","20":"tag-saamanya-pela","21":"tag-samanya-pela","22":"tag-wurthaya","23":"tag-3666","24":"tag-3665"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts\/10698"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/users\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/comments?post=10698"}],"version-history":[{"count":6,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts\/10698\/revisions"}],"predecessor-version":[{"id":11235,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/posts\/10698\/revisions\/11235"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/media\/11442"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/media?parent=10698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/categories?post=10698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/ol\/wp-json\/wp\/v2\/tags?post=10698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}