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concurrent wanted, hexagon related 2017 Ecuador NMO (OMEC) 3.6

Source:

September 18, 2021

geometryhexagonconcurrencyconcurrent

Problem Statement

Let

ABCDEF

be a convex hexagon with sides not parallel and tangent to a circle

\Gamma

at the midpoints

P

,

Q

,

R

of the sides AB,

CD

,

EF

respectively.

\Gamma

is tangent to

BC

,

M

and

FA

at the points

X, Y, Z

respectively. Line

AB

intersects lines

EF

and

CD

at points

M

and

N

respectively. Lines

MZ

and

NX

intersect at point

K

. Let

r

be the line joining the center of

\Gamma

and point

K

. Prove that the intersection of

PY

and

QZ

lies on the line

r

.

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