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Elementary Geometry for Mathematical Olympiads

Source: Indonesia RMO 2022, Essay No 4

August 24, 2022

geometryIndonesiaRMO2022circumcirclegeometric transformationreflection

Problem Statement

Suppose

ABC

is a triangle with circumcenter

O

. Point

D

is the reflection of

A

with respect to

BC

. Suppose

\ell

is the line which is parallel to

BC

and passes through

BD

. The line through

B

and parallel to

CD

meets

\ell

at

B_1

. Lines

CB_1

and

BC_1

intersect at point

B_2

. The line through

C

parallel to

BD

and

\ell

meet at

C_1

. Finally,

BC_1

and

CD

intersects at point

C_2

. Prove that points

A, B_2, C_2, D

lie on a circle.

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