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CBSE Class 9 Answered

In the fig. ABCD is a quadrilateral inscribed in a circle with centre o. CD is produced to E suh that angleAED=95 and angleOBA=30. Findangle OAC
Asked by kumar.ashlesha | 16 Jan, 2015, 10:29: PM
answered-by-expert Expert Answer
G i v e n space t h a t space angle A D E equals 95 degree angle A D E space a n d space angle A D C space a r e space s u p p l e m e n t a r y a n g l e s. T h u s comma space w e space h a v e comma angle A D C equals 180 degree minus 95 degree equals 85 degree A l s o space w e space h a v e comma space q u a d. space A B C D space i s space a space c y c l i c space q u a d r i l a t e r a l. T h u s comma angle A B C space a n d space angle A D C space a r e space s u p p l e m e n t a r y. rightwards double arrow angle A B C equals 180 degree minus 85 degree equals 95 degree H e r e comma space O space i s space t h e space c e n t r e space o f space t h e space c i r c l e comma space O A comma space O B space a n d space O C space a r e space t h e space r a d i i space o f space t h e space c i r c l e. rightwards double arrow O A equals O B equals O C rightwards double arrow triangle A O B space i s space a n space i s o s c e l e s space t r i a n g l e rightwards double arrow angle O A B equals angle O B A equals 30 degree space left parenthesis g i v e n right parenthesis S i n c e space angle A B C equals 95 degree comma space angle O B C equals angle A B C minus angle O B A equals 95 degree minus 30 degree equals 65 degree S i m i l a r l y comma space triangle B O C space i s space a n space i s o s c e l e s space t r i a n g l e. T h e r e f o r e comma space angle O B C equals angle O C B equals 65 degree S u m space o f space a n g l e s space i n space a space t r i a n g l e space i s space 180 degree. therefore F r o m space triangle B O C comma space angle B O C equals 180 degree minus angle O B C minus angle O C B rightwards double arrow angle B O C equals 180 degree minus 65 degree minus 65 degree rightwards double arrow angle B O C equals 50 degree angle A O B equals 180 degree minus 2 cross times 30 degree equals 120 degree angle A O C equals angle A O B plus angle B O C rightwards double arrow angle A O C equals 120 degree plus 50 degree equals 170 degree S i n c e space O A equals O C comma space triangle A O C space i s space a n space i s o s c e l e s space t r i a n g l e comma space a n d space h e n c e space b a s e space a n g l e s space a r e space e q u a l. T h u s comma space angle O A C equals fraction numerator 180 degree minus 170 degree over denominator 2 end fraction equals fraction numerator 10 degree over denominator 2 end fraction equals 5 degree
Answered by Vimala Ramamurthy | 17 Jan, 2015, 11:31: AM

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