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2014 JBMO Shortlist G5

Source: 2014 JBMO Shortlist G5

October 8, 2017

geometryJBMO

Problem Statement

Let

ABC

be a triangle with

{AB\ne BC}

; and let

{BD}

be the internal bisector of

\angle ABC,\

,

{AB}

. Denote by

{M}

the midpoint of the arc

{AC}

which contains point

{B}

. The circumscribed circle of the triangle

{\vartriangle BDM}

intersects the segment

{AB}

at point

{K\neq B}

. Let

{J}

be the reflection of

{A}

with respect to

{K}

. If

{DJ\cap AM=\left\{O\right\}}

, prove that the points

{J, B, M, O}

belong to the same circle.

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