MathDB

4 points defined be equal ratios in a triangle, collinearity wanted

Source: Mexican Mathematical Olympiad 1997 OMM P2

July 28, 2018

ratiogeometrycollinear

Problem Statement

In a triangle

ABC, P

and

P'

are points on side

BC, Q

on side

CA

, and

R

on side

AB

, such that

\frac{AR}{RB}=\frac{BP}{PC}=\frac{CQ}{QA}=\frac{CP'}{P'B}

. Let

G

be the centroid of triangle

ABC

and

K

be the intersection point of

AP'

and

RQ

. Prove that points

P,G,K

are collinear.