MathDB

Weird circle passes through a fixed point

Source: Own

June 21, 2023

geometryFixed point

Problem Statement

Let

\triangle ABC

be a triangle such that

AB = AC

, and let its circumcircle be

\Gamma

. Let

\omega

be a circle which is tangent to

AB

and

AC

at

R

and

X

. Point

Y

belongs to

BR

, and lines

PB

and

PC

intersect

\Gamma

again at

Q

and

R

.

X

and

Y

are points on lines

BR

and

CQ

such that

AX = XB

and

AY = YC

. Show that as

P

varies on

\omega

, the circumcircle of

\triangle AXY

passes through a fixed point other than

A

.

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