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CBSE Class 9 Answered

In the figure, chord AB of circle with centre O, is produced to C such that BC = OB. CO is joined and produced to meet the circle in D. If ACD = y and AOD = x, show that x = 3y.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

In OBC, OB = BC

BOC = BCO = y (angles opp. to equal sides are equal)

ABO is the exterior angle of BCO

So, ABO = 2y (ext. angle is equal to the sum of int. opp. Angles)

ABO = BAO (OA and OB are radius of same circle)

Similarly, AOD is the exterior angle of AOC.

AOD = BAO + ACO

= 2y + y = 3y

Answered by | 04 Jun, 2014, 03:23: PM

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