A geometry problem by A Former Brilliant Member

Geometry Level 1

Circle $O$ is inscribed in $\triangle ABC,$ as shown in the figure above. The points of tangency are at $D,E,$ and $F$ . Given that $AD=2$ and $DC=3$ , find the area of $\triangle ABC$ .

The answer is 6.

1 solution

A Former Brilliant Member
Jul 10, 2017

Let $EB=BF=x$ . By Pythagorean theorem , we have

$25=(x+2)^2+(x+3)^2$

$25=x^2+4x+4+x^2+6x+9$

Simplifying further, we get

$x^2+5x-6=0$

By factoring, we get

$x=1$

Finally, the area of $\triangle ABC$ is $\dfrac{1}{2}(BC)(AB)=\dfrac{1}{2}(4)(3)=$ $\boxed{6}$

What a nice problem. Waiting for another.

christian reivan - 3 years ago

A geometry problem by A Former Brilliant Member

The answer is 6.

1 solution

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