MathDB

4. A triangle

A B C

with angle

A

equal to

60^{\circ}

is given. Its incircle is tangent to side

A B

at point

D

, while its excircle tangent to side

A C

, is tangent to the extension of side

A B

at point

E

. Prove that the perpendicular to side

A C

, passing through point

D

, meets the incircle again at a point equidistant from points

E

and

C

. (The excircle is the circle tangent to one side of the triangle and to the extensions of two other sides.) Azamat Mardanov

Problem Statement