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1994 OIM Problems/Problem 4

Revision as of 14:29, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Points <math>A</math>, <math>B</math> and <math>C</math> are given on a circle <math>K</math> so that triangle <math>ABC</math> is acute. Let <math>P</math> be a...")
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Problem

Points $A$, $B$ and $C$ are given on a circle $K$ so that triangle $ABC$ is acute. Let $P$ be a point interior to $K$. The lines $AP$, $BP$ and $CP$ are drawn, which again cut the circle at $X$, $Y$ and $Z$. Determine the point $P$ so that the triangle $XYZ$ is equilateral.

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

Solution

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See also

https://www.oma.org.ar/enunciados/ibe9.htm

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