Question

A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ.

Answer 1

Given: Chord PQ is parallel to tangent at R.

To prove: R bisects the arc PRQ.

Proof: ∠1 = ∠2  ...[Alternative interior angles]

∠1 = ∠3  ...[Angle between tangent and chord is equal to angle made by chord in alternative segment]

∴ ∠2 = ∠3

⇒ PR = QR  ...[Sides opposite to equal angles are equal]

⇒ PR = QR 

So, R bisects PQ.