MathDB

2016 JBMO Shortlist G2

Source: 2016 JBMO Shortlist G2

October 8, 2017

geometryJBMO

Problem Statement

Let

{ABC}

be a triangle with

\angle BAC={{60}^{{}^\circ }}

. Let

D

and

{ADE}

be the feet of the perpendiculars from

{A}

to the external angle bisectors of

\angle ABC

and

\angle ACB

, respectively. Let

{O}

be the circumcenter of the triangle

{ABC}

. Prove that the circumcircles of the triangles

{ADE}

and

{BOC}

are tangent to each other.

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