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common chord of the circumcircles passes through point

Source: All Russian MO 1994 ARO XI P3

July 29, 2018

geometrytangent

Problem Statement

Two circles

S_1

and

S_2

touch externally at

F

. their external common tangent touches

S_1

at A and

S_2

B

. A line, parallel to

AB

and tangent to

S_2

C

, intersects

S_1

D

and

E

. Prove that the common chord of the circumcircles of triangles

ABC

and

BDE

passes through point

F

.
(A. Kalinin)