MathNet 2007-part-02 — 187 problems (EN–VI) Question 150

A circle is inscribed in $\triangle ABC$ with sides $AB = 4$, $BC = 6$, and $AC = 8$. If $P$ and $Q$ are the respective points of tangency of $\overline{AB}$ and $\overline{AC}$ with the circle, determine the length of chord $PQ$.