MathDB

Let

ABC

be an acute scalene triangle. Let

D

be the foot of the

A

-bisectrix and

E

be the foot of the

A

-altitude. The perpendicular bisector of the segment

AD

intersects the semicircles of diameter

AB

and

AC

which lie on the outside of triangle

ABC

X

and

Y

respectively. Prove that the points

X,Y,D

and

E

lie on a circle.

Problem Statement