# Collinear points

• Dec 21st 2006, 02:33 AM
malaygoel
Collinear points
ABC is an acute triangle(all the three angles are acute).
D,E,F are points on BC,CA,AB respectively such that AD,BE,CF are the altitudes of the triangle.
FP is perpendicular to BC, P lying on BC
FQ is perpendicualr to AC, Q lying on AC
FN is perpendicualr to BE, N lying on BE
Prove that P,Q,M,N are collinear points.

Keep Smiling
Malay
• Dec 21st 2006, 03:19 AM
CaptainBlack
Quote:

Originally Posted by malaygoel
ABC is an acute triangle(all the three angles are acute).
D,E,F are points on BC,CA,AB respectively such that AD,BE,CF are the altitudes of the triangle.
FP iis perpendicular to BC, P lying on BC
FQ is perpendicualr to AC, Q lying on AC
PQ interscts AD at M and BE at N.
Prove that P,Q,M,N are collinear points.

Keep Smiling
Malay

There is nothing to prove:

"PQ interscts AD at M and BE at N"

Puts M and N on the segment PQ, so P,Q,M and N are colinear

A puzzled RonL
• Dec 26th 2006, 10:46 PM
malaygoel
Quote:

Originally Posted by CaptainBlack
There is nothing to prove:

"PQ interscts AD at M and BE at N"

Puts M and N on the segment PQ, so P,Q,M and N are colinear

A puzzled RonL

Sorry:eek:
I will edit the the first post