The Three Circles

Geometry Level 2

3 Circles $\Gamma_A, \Gamma_B$ and $\Gamma_C$ have radii of $2 \mbox{ m}, 3\mbox{ m}$ and $10\mbox{ m}$ respectively. Each circle is tangential to the other two. The centers of the circles are $A, B$ and $C$ , respectively. What is the area (in $\mbox{m}^2$ ) of triangle $ABC$ ?

The answer is 30.

1 solution

Arron Kau Staff
May 13, 2014

Observe that $AB = 5, AC = 12$ and $BC = 13$ . Hence, $ABC$ is a right angle triangle, thus the area is $\frac {1}{2}\times 5 \times 12 = 30$ .

The Three Circles

The answer is 30.

1 solution

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