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2011 JBMO Shortlist G4

Source: 2011 JBMO Shortlist G4

October 8, 2017

geometryJBMO

Problem Statement

Point

{D}

lies on the side

{BC}

of

\vartriangle ABC

. The circumcenters of

\vartriangle ADC

and

\vartriangle BAD

are

{O_1}

and

{O_2}

, respectively and

{O_1O_2\parallel AB}

. The orthocenter of

\vartriangle ADC

is

2m\left( \angle C \right)=3m\left( \angle B \right).

and

{AH=O_1O_2}.

Find the angles of

\vartriangle ABC

if

2m\left( \angle C \right)=3m\left( \angle B \right).

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