## Problem of the Day #319: Circles in Triangles in Quadrilaterals
*February 1, 2012*

*Posted by Alex in : potd , trackback*

Two triangles share a hypotenuse and do not overlap. There is a quadrilateral whose vertices are the four unique vertices of the two triangles. The inradius of one triangle is $a$ and the area of the quadrilateral is $b$ times the area of that same triangle. Find the inradius of the other triangle in terms of $a$ and $b$.

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