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RD Sharma Solutions Class 10 Mathematics Solutions for Circles Exercise 10.2 in Chapter 10 - Circles

Question 3 Circles Exercise 10.2

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.

Answer:

Solution:

R D Sharma Solutions - Mathematics - Class 10 chapter Circles  Question 3 Solution image

Given: Chord PQ is parallel to tangent at R.

To prove: R bisects the arc PRQ.

Proof:

Since PQ || tangent at R.

∠1 = ∠2 [alternate interior angles]

∠1 = ∠3[angle between tangent and chord is equal to angle made by chord in alternate segment]

So, ∠2 = ∠3

⇒ PR = QR [sides opposite to equal angles are equal]

Hence, clearly R bisects the arc PRQ.

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