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Ab and Cd Are Common Tangents to Two Circles of Equal Radii. Prove that Ab = Cd. - Mathematics

Short Note

AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.

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Solution

Given: Two circles with centre’s O and O'. AB and CD are common tangents to the circles which intersect in P.

To Prove: AB = CD

Proof:

AP = PC (length of tangents drawn from an external point to the circle are equal)                              ..… (1) 

PB = PD (length of tangents drawn from an external point to the circle are equal)                              ..… (2) 

Adding (1) and (2), we get

AP + PB = PC + PD

⇒ AB = CD
Hence Proved

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.2 | Q 38 | Page 38
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