MathDB

fixed point, intersection of line with circle

Source: Switzerland - Swiss ΜΟ 2019 p1

July 14, 2020

geometryFixed pointfixedcircle

Problem Statement

Let

A

be a point and let k be a circle through

A

. Let

B

and

C

be two more points on

k

. Let

X

be the intersection of the bisector of

\angle ABC

with

k

. Let

Y

be the reflection of

A

wrt point

X

, and

D

the intersection of the straight line

YC

with

k

. Prove that point

D

is independent of the choice of

B

and

C

on the circle

k

.

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