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2009 JBMO Shortlist G5

Source: 2009 JBMO Shortlist G5

October 8, 2017

geometryJBMO

Problem Statement

Let

{A, B, C}

and

{O}

be four points in plane, such that

\angle ABC>{{90}^{{}^\circ }}

and

{OA=OB=OC}

.Define the point

{D\in AB}

and the line

{l}

such that

{E}

and

{l\perp AO}

. Line

{l}

cuts

{AC}

at

{E}

and circumcircle of

{ABC}

at

{F}

. Prove that the circumcircles of triangles

{BEF}

and

{CFD}

are tangent at

{F}

.

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