This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

1998 Taiwan National Olympiad, 4
Tags: geometry , incenter , geometry unsolved , Taiwan , 1998 , #4 , geometric inequality
Let $I$ be the incenter of triangle $ABC$. Lines $AI$, $BI$, $CI$ meet the sides of $\triangle ABC$ at $D$, $E$, $F$ respectively. Let $X$, $Y$, $Z$ be arbitrary points on segments $EF$, $FD$, $DE$, respectively. Prove that $d(X, AB) + d(Y, BC) + d(Z, CA) \leq XY + YZ + ZX$, where $d(X, \ell)$ denotes the distance from a point $X$ to a line $\ell$.