AB is a diameter and AC is a chord of a circle with centre O such that BAC =
. The tangent at C intersects extended AB at a point D. Prove that BC = BD.
Solution
Given AB is a diameter and AC is a chord of circle with center O.
To Prove : BC = BD
Construction : Join B and C
Proof :[Angle is alternate segment]
[Angle in semi circle formed is 90°]
In ABC
[Sum of interior angles of a triangle is 180°]
Also , [Linear pair]
In
From equation (i) and (ii)
[
Sides opposite to equal angles are equal]
Hence Proved