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BC is tangent to circumcircle of BDE, isosceles ABC

Source: 2021 Austrian Regional Competition For Advanced Students p2

May 31, 2021

geometrytangentisoscelesAZE CMO TSTAZE EGMO TST

Problem Statement

Let

ABC

be an isosceles triangle with

AC = BC

and circumcircle

k

. The point

D

lies on the shorter arc of

k

over the chord

BC

and is different from

B

and

C

. Let

E

denote the intersection of

CD

and

AB

. Prove that the line through

B

and

C

is a tangent of the circumcircle of the triangle

BDE

.
(Karl Czakler)