MathDB

Russian geo showing its reputation again

Source: RMM Extralist 2021 G3

September 18, 2023

RMM ShortlistgeometryRussian

Problem Statement

Let

\Omega

be the circumcircle of a triangle

ABC

with

\angle BAC > 90^{\circ}

and

AB > AC

. The tangents of

\Omega

at

B

and

C

cross at

D

and the tangent of

\Omega

at

A

crosses the line

BC

at

E

. The line through

D

, parallel to

AE

, crosses the line

BC

at

F

. The circle with diameter

EF

meets the line

AB

at

P

and

Q

and the line

AC

at

X

and

Y

. Prove that one of the angles

\angle AEB

,

\angle PEQ

,

\angle XEY

is equal to the sum of the other two.

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