1990 OIM Problems/Problem 2

Revision as of 13:36, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == In a triangle <math>ABC</math>, let <math>I</math> be the center of the inscribed circle and <math>D</math>, <math>E</math> and <math>F</math> be its points of t...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

In a triangle $ABC$, let $I$ be the center of the inscribed circle and $D$, $E$ and $F$ be its points of tangency with the sides $BC$, $AC$ and $AB$, respectively. Let $P$ be the other point of intersection of the line $AD$ with the inscribed circle.

If $M$ is the midpoint of $EF$, show that the four points $P$, $I$, $M$ and $D$ belong to the same circle.

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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://www.oma.org.ar/enunciados/ibe5.htm