MathDB

Geometry with three circles

Source: Kvant Magazine No. 6 2020 M2606

March 9, 2023

geometryKvant

Problem Statement

Three circles

\omega_1,\omega_2

and

\omega_3

pass through one point

D{}

. Let

A{}

be the intersection of

\omega_1

and

\omega_3

, and

E{}

be the intersections of

\omega_3

and

\omega_2

and

F{}

be the intersection of

\omega_2

and

\omega_1

. It is known that

\omega_3

passes through the center

B{}

of the circle

\omega_2

. The line

EF

intersects

\omega_1

a second time at the point

G{}

. Prove that

\angle GAB=90^\circ

.
Proposed by K. Knop

Back to Problems View on AoPS