MathDB

Let

ABC

be an acute-angled triangle whose inscribed circle touches

AB

and

AC

D

and

E

respectively. Let

X

and

Y

be the points of intersection of the bisectors of the angles

\angle ACB

and

\angle ABC

with the line

DE

and let

Z

be the midpoint of

BC

. Prove that the triangle

XYZ

is equilateral if and only if

\angle A = 60^\circ

Problem Statement