MathDB

Assume that all angles of a triangle

ABC

are acute. Let

D

and

E

be points on the sides

AC

and

BC

of the triangle such that

A, B, D,

and

E

lie on the same circle. Further suppose the circle through

D,E,

and

C

intersects the side

AB

in two points

X

and

Y

. Show that the midpoint of

XY

is the foot of the altitude from

C

AB

Problem Statement