MathDB

P6 Cono Sur 2021

Source: Cono Sur 2021 #6

December 1, 2021

geometry

Problem Statement

Let

ABC

be a scalene triangle with circle

\Gamma

. Let

P,Q,R,S

distinct points on the

BC

side, in that order, such that

\angle BAP = \angle CAS

and

\angle BAQ = \angle CAR

. Let

U, V, W, Z

be the intersections, distinct from

A

, of the

AP, AQ, AR

and

AS

with

\Gamma

, respectively. Let

X = UQ \cap SW

,

Y = PV \cap ZR

,

T = UR \cap VS

and

K = PW \cap ZQ

. Suppose that the points

M

and

N

are well determined, such that

M = KX \cap TY

and

N = TX \cap KY

. Show that

M, N, A

are collinear.

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