MathDB

3

Part of 2017 USAJMO

Problems(1)

Equilateral triangle $ABC$, $DEF$ has twice the area

Source: JMO 2017 Problem 3, Titu, Luis, Cosmin

4/19/2017
Let ABCABC be an equilateral triangle, and point PP on its circumcircle. Let PAPA and BCBC intersect at DD, PBPB and ACAC intersect at EE, and PCPC and ABAB intersect at FF. Prove that the area of △DEF\triangle DEF is twice the area of △ABC\triangle ABC.
Proposed by Titu Andreescu, Luis Gonzales, Cosmin Pohoata
geometryUsa j mo2017 USAJMOUSAJMO