MathDB

Rio Geo.

Source: Rioplatense Olympiad L3 2019

December 10, 2019

geometry

Problem Statement

Let

ABC

be a triangle with

AB<AC

and circuncircle

\omega

. Let

M

and

N

be the midpoints of

AC

and

GP

respectively and

G

is the centroid of

ABC

. Let

P

be the foot of perpendicular of

A

to the line

BC

, and the point

Q

is the intersection of

GP

and

\omega

(

Q,P,G

are collinears in this order). The line

QM

cuts

\omega

in

M_1

and the line

CN_1

cuts

\omega

in

N_1

. If

K

is the intersection of

BM_1

and

CN_1

prove that

P

,

G

and

K

are collinears.

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