MathDB

11

Part of 2013 Baltic Way

Problems(1)

Projections

Source: 2013 Baltic Way, Problem 11

12/31/2013
In an acute triangle ABCABC with AC>ABAC > AB, let DD be the projection of AA on BCBC, and let EE and FF be the projections of DD on ABAB and ACAC, respectively. Let GG be the intersection point of the lines ADAD and EFEF. Let HH be the second intersection point of the line ADAD and the circumcircle of triangle ABCABC. Prove that AGā‹…AH=AD2AG \cdot AH=AD^2
geometrycircumcircletrigonometrygeometry unsolved