MathDB

BMO 2021 problem 1

Source: Balkan MO 2021 P1

September 8, 2021

Problem Statement

Let

ABC

be a triangle with

AB<AC

. Let

\omega

be a circle passing through

B, C

and assume that

A

is inside

\omega

. Suppose

X, Y

lie on

\omega

such that

\angle BXA=\angle AYC

. Suppose also that

X

and

C

lie on opposite sides of the line

AB

and that

Y

and

B

lie on opposite sides of the line

AC

. Show that, as

X, Y

vary on

\omega

, the line

XY

passes through a fixed point.
Proposed by Aaron Thomas, UK

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