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.

Provided in question: Chord PQ is parallel to tangent at R.

To prove: R bisects the arc PRQ.

Proof:

Since PQ || tangent at R.

 [alternate interior angles]
[angle between tangent and chord is equal to angle made by chord in alternate segment]

So,

Hence, clearly R bisects the arc PRQ.