Area of Triangle PQR

Geometry Level 2

In the diagram, the circles with centers P , Q , R P, Q, R have radii 3 , 2 , and 1 3, 2, \text{ and} \ 1 respectively. Each circle touches the other two as shown. What is the area of triangle P Q R PQR ?

10 12 8 6 9

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Feb 13, 2017

Notice that R Q = 3 RQ = 3 , P R = 4 PR= 4 and P Q = 5 PQ=5

Thus triangle P Q R PQR is a right triangle and the area 3 × 4 2 = 6 \frac{3\times 4}{2}= 6

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