Geometry - Perimeter of Triangle of Circle Centers

CAT 1998 Slot 1 · Quantitative Ability · Medium · Geometry

This is a medium Quantitative Ability question from the CAT 1998 Slot 1 paper. It tests Geometry. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

Three circles, each of radius 20, have centres at $P$, $Q$ and $R$. Further, $AB = 5$, $CD = 10$ and $EF = 12$. What is the perimeter of $\Delta PQR$?

1. A.

   120

2. B.

   66

3. C.

   93

4. D.

   87

Answer & explanation hiddenTry it firstShow answer

Answer

C

Explanation

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

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