KVPY SA Exam 2014 Question Paper

Question : 9 of 80

Marks: +1, -0

Suppose S

_1

and S

_2

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

Validate

Solution:

AR = PR = 10 -x

PQ = 10 - 2x

AB = CD = 10

CD = CS + SD = y + SD

= y + SP + PQ

10 = y + y + 10 - 2x

⇒ y = x

Now

RS = SP + PQ + QR

= y + 10 - 2x + x

= 10 + y -x = 10

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