In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length of $\overline{XY}$.

RedDragonl Jul 31, 2024

#1**+1 **

mmm...let's note something really quickly.

In the problem, it said that

\(QR + PR < PQ \)

However, it said that PQR is a triangle, but this violates the Triangle Inequality Theorem.

So this problem is invalid.

thanks! :)

NotThatSmart Jul 31, 2024