MathDB

Prove that points $M, N$ and $P$ are collinear.

Source: Moldova TST 1995

August 8, 2023

geometry

Problem Statement

Each pair of three circles have the common chords

AA_1, BB_1

and

CC_1{}

such that lines

AB{}

and

A_1B_1

intersect in point

M{}

,

BC

and

B_1C_1

intersect in point

N{}

,

CA{}

and

C_1A_1

intersect in point

P{}

. Prove that points

M, N

and

P

are collinear.

Back to Problems View on AoPS