MathDB

5

Part of 2016 USAJMO

Problems(1)

Inversely Similiar Triangles

Source: JMO/5 2016

4/20/2016
Let △ABC\triangle ABC be an acute triangle, with OO as its circumcenter. Point HH is the foot of the perpendicular from AA to line BC↔\overleftrightarrow{BC}, and points PP and QQ are the feet of the perpendiculars from HH to the lines AB↔\overleftrightarrow{AB} and AC↔\overleftrightarrow{AC}, respectively.
Given that AH2=2⋅AO2,AH^2=2\cdot AO^2, prove that the points O,P,O,P, and QQ are collinear.
geometrysimilar triangles2016 USAJMOUSAJMOUSA(J)MOisogonal conjugatesAngle Chasing