MathDB

Projections

Source: 2013 Baltic Way, Problem 11

December 31, 2013

geometrycircumcircletrigonometrygeometry unsolved

Problem Statement

In an acute triangle

ABC

with

AC > AB

, let

D

be the projection of

A

on

BC

, and let

E

and

F

be the projections of

D

on

ABC

and

AC

, respectively. Let

G

be the intersection point of the lines

AD

and

EF

. Let

H

be the second intersection point of the line

AD

and the circumcircle of triangle

ABC

. Prove that

AG \cdot AH=AD^2

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