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1995 OIM Problems/Problem 5

Revision as of 14:51, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == The circle inscribed in the triangle <math>ABC</math> is tangent to <math>BC</math>, <math>CA</math>, and <math>AB</math> at <math>D</math>, <math>E</math>, and...")
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Problem

The circle inscribed in the triangle $ABC$ is tangent to $BC$, $CA$, and $AB$ at $D$, $E$, and $F$ respectively. Suppose that said circle cuts $AD$ again at its midpoint $X$, that is, $AX = XD$. The lines $XB$ and $XC$ again cut the circle inscribed in $Y$ and $Z$, respectively.

Prove that $EY = FZ$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe10.htm

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