Question

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Answer 1

Let RA and RB be two tangents to the circle with center O and let AB be a chord of the circle.

We have to prove that ∠RAB = ∠RDA.

 Now, RA = RB (Since tangents drawn from an external point to a circle are equal) 

In. ΔRAB,  ∠RAB = ∠RDA , (Since opposite sides are equal, their base angles are also equal)