Question

In the given figure,AB is a chord of a circle with centre O and AB is produced to C such that BC= OB. Also, CO is joined and produced to meet the circle in D. If angle ACD = 25⁰ then angle AOD =

Answer 1

AB is a chord of a circle with centre O AB is produced to C such that BO = BC 

CO is joined and produced to meet the circle at D

We shall prove x∘=3y∘ 

We have 

BC=OB

∠OCB=∠BOC=y∘

[Angles opposite to equal sides are equal ]

∠OBA=∠BOC+∠OCB

[Ext angle of a △ is equal to the sum of the opposite interior angles ]

⇒∠OBC=y∘+y∘=2y∘

OA=OB...[Radii of the same circle ]

∠OAB=∠OBA....[Angles opp. To equal sides of a △]

=2y∘

∠AOD=∠OAC+∠OCA

=2y∘+y∘

=3y∘     [Exterior angle - Sum of opposite interrior angles]