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Parallelogram to find angle

Source: All Russian MO 2015, grade 10, problem 2

August 7, 2015

geometrycircumcircleparallelogram

Problem Statement

Given is a parallelogram

ABCD

, with

AB <AC <BC

. Points

E

and

F

are selected on the circumcircle

\omega

of

ABC

so that the tangenst to

\omega

at these points pass through point

D

and the segments

AD

and

CE

intersect. It turned out that

\angle ABF = \angle DCE

. Find the angle

\angle{ABC}

. A. Yakubov, S. Berlov

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