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Question

Suppose S1 and S2 are two unequal circles; AB and CD are the direct common tangents to these circles. A transverse common tangent PQ cuts AB at R and CD at S. If AB = 10, then RS is


A

8

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B

11

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C

10

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D

9

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Solution

The correct option is C

10


Let RB be α and PS be β

∴ RP = RA = 10- α RS = 10 - α + β ...... (1)

Also SQ = SD = 10 - β RS = 10 - β + α .......(2)

(1) and (2) α = β , Hence RS = 10


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