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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.
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.
CBSE | Circles | Class 10 | Exercise 10.2 | Maths | RD Sharma
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.

$\angle 1=\angle 2$  [alternate interior angles]
$\angle 1=\angle 3$ [angle between tangent and chord is equal to angle made by chord in alternate segment]

So, $\angle 2=\angle 3$

$\Rightarrow PR=QR$

Hence, clearly R bisects the arc PRQ.

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