Concurrent Segments In A Triangle
Problem
Consider triangle $ABC$ and the segments joining the points $X$, $Y$, and $Z$, on opposite edges.
Prove that the segments $AX$, $BY$, and $CZ$ are concurrent at $P$ if and only if $\dfrac{AZ}{BZ}\dfrac{BX}{CX}\dfrac{CY}{AY} = 1$.
Problem ID: 316 (18 Mar 2007) Difficulty: 4 Star