MathDB

2016 JBMO Shortlist G5

Source: 2016 JBMO Shortlist G5

October 8, 2017

geometryJBMO

Problem Statement

Let

ABC

be an acute angled triangle with orthocenter

{H}

and circumcenter

{O}

. Assume the circumcenter

{X}

of

{BHC}

lies on the circumcircle of

{ABC}

. Reflect

O

across

{X}

to obtain

{O'}

, and let the lines

{XH}

and

{O'A}

meet at

{K}

. Let

L,M

and

N

be the midpoints of

\left[ XB \right],\left[ XC \right]

and

\left[ BC \right]

, respectively. Prove that the points

K,L,M

and

{N}

are concyclic.

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