Geometry - Perimeter of Triangle of Circle Centers

CAT 1998 Slot 1 · QA · Medium · Geometry

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Three circles, each of radius 20, have centres at PP, QQ and RR. Further, AB=5AB = 5, CD=10CD = 10 and EF=12EF = 12. What is the perimeter of ΔPQR\Delta PQR?

  1. A.

    120

  2. B.

    66

  3. C.

    93

  4. D.

    87

Answer

C

Explanation

PQ=PE+FQ−FE=20+20−12=28PQ = PE + FQ - FE = 20 + 20 - 12 = 28 QR=20+20−CD=40−10=30QR = 20 + 20 - CD = 40 - 10 = 30 PR=20+20−AB=40−5=35PR = 20 + 20 - AB = 40 - 5 = 35

Perimeter of ΔPQR=28+30+35=93\Delta PQR = 28 + 30 + 35 = 93.

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