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A chord PQ of a circle is parallel to t...

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.`

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Given Chord PQ is parallel to tangent at R.
To prove R bisects the are PRQ

Proof `angle1=angle2` [alternate interior angles]
`angle1=angle3`
[angle between tangent and chord is equal to angle made by chord in alternate segment]
`:.angle2=angle3`
`rArrPR=QR` [sides opposite to equal angles are equal]
`rArrPR=QR`
So, R bisects PQ.
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