MathDB

Two circles through A and O

Source: Baltic Way 2022/11

November 12, 2022

geometry

Problem Statement

Let

ABC

be a triangle with circumcircle

\Gamma

and circumcentre

O

. The circle with centre on the line

AB

and passing through the points

A

and

O

intersects

\Gamma

again in

D

. Similarly, the circle with centre on the line

AC

and passing through the points

A

and

O

intersects

\Gamma

again in

E

. Prove that

BD

is parallel with

CE

.

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