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. - Mathematics

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Sum

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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Chapter 9: Circles - Exercise 9.3 [Page 107]

APPEARS IN

NCERT Exemplar Mathematics Class 10
Chapter 9 Circles
Exercise 9.3 | Q 8 | Page 107
RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.2 | Q 7 | Page 33

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