MathDB

IV Lusophon Mathematical Olympiad 2014 - Problem 3

Source:

December 28, 2014

geometry

Problem Statement

In a convex quadrilateral

ABCD

P

and

Q

are points on sides

BC

and

DC

such that

B\hat{A}P = D\hat{A}Q

. If the line that passes through the orthocenters of

\triangle ABP

and

\triangle ADQ

is perpendicular to

AC

, prove that the area of these triangles are equals.