MathDB

midpoint is foot of altitude (Kharkiv City X 2012 - Ukr)

Source:

March 10, 2020

geometryaltitudeKharkivmidpointConcyclic

Problem Statement

In the acute-angled triangle

ABC

on the sides

AC

and

BC

, points

D

and

E

are chosen such that points

A, B, E

, and

D

lie on one circle. The circumcircle of triangle

DEC

intersects side

AB

at points

X

and

Y

. Prove that the midpoint of segment

XY

is the foot of the altitude of the triangle, drawn from point

C