## 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

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