MathDB

INMO 2018 -- Problem #3

Source: INMO 2018

January 21, 2018

geometry

Problem Statement

Let

\Gamma_1

and

\Gamma_2

be two circles with respective centres

O_1

and

O_2

intersecting in two distinct points

A

and

B

such that

\angle{O_1AO_2}

is an obtuse angle. Let the circumcircle of

\Delta{O_1AO_2}

intersect

\Gamma_1

and

\Gamma_2

respectively in points

C (\neq A)

and

D (\neq A)

. Let the line

CB

intersect

\Gamma_2

in

E

; let the line

DB

intersect

\Gamma_1

in

F

. Prove that, the points

C, D, E, F

are concyclic.

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