2017 USAJMO Problems/Problem 3

Revision as of 19:13, 19 April 2017 by Thedoge (talk | contribs) (Created page with "==Problem== (<math>*</math>) Let <math>ABC</math> be an equilateral triangle and let <math>P</math> be a point on its circumcircle. Let lines <math>PA</math> and <math>PB</mat...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

($*$) Let $ABC$ be an equilateral triangle and let $P$ be a point on its circumcircle. Let lines $PA$ and $PB$ intersect at $D$; let lines $PB$ and $CA$ intersect at $E$; and let lines $PC$ and $AB$ intersect at $F$. Prove that the area of triangle $DEF$ is twice that of triangle $ABC$.