Inscribed triangle

Geometry Level 1

Triangle $ABC$ , with obtuse angle $B$ , is inscribed in a circle. Altitude $CH$ of the triangle is tangent to the circle. If $AB=8$ and $BH=10$ , find the radius of the circle.

The answer is 14.

1 solution

Danish Ahmed
Jan 17, 2015

Let $O$ be the center of the circle. Triangle $AOB$ is an isosceles triangle with vertex $O$ . Construct altitude $OX$ . $OCHX$ is a rectangle. $XB=4$ so $XH=OC=14$

Inscribed triangle

The answer is 14.

1 solution

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