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In Fig Common Tangents Pq and Rs to Two Circles Intersect at A. Prove that Pq = Rs. - CBSE Class 10 - Mathematics

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Question

In fig common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

Solution

Consider

Two circles namely (i) & (ii) as shown with common tangents as PQ and RS.

We know that

The tangents from external point to the circle are equal in length.

From A to circle (i) AP = AR … (i)

From A to circle (ii), AQ = AS …. (ii)

(i) + (ii) ⇒ AP + AQ = AR + RS

⇒ PQ = RS

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Solution In Fig Common Tangents Pq and Rs to Two Circles Intersect at A. Prove that Pq = Rs. Concept: Circles Examples and Solutions.
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