MathDB

A point

D

is taken on the side

BC

of an acute-angled triangle

ABC

such that

AB = AD

. Point

E

on the altitude from

C

of the triangle is such that the circle

k_1

with center

E

is tangent to the line

AD

D

. Let

k_2

be the circle through

C

that is tangent to

AB

B

. Prove that

A

lies on the line determined by the common chord of

k_1

and

k_2

Problem Statement