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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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#### Solution

**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.

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