Question

AB is a chord of a circle and CT, the tangent at C, is parallel to AB. Prove that $CA=CB$.

Answer 1

According to the alternate segment theorem, angle between a tangent and a chord through a point of contact is equal to the angle in the alternate segment.

$⟹\angle TCB=\angle CAB$ -eq.

Given $CT\parallel AB$

$⟹\angle TCB=\angle CBA$$ -eq.2

From eq.1 and eq.2

$\angle CAB=\angle CBA$

$⟹CA=CB$