MathDB

concurrency of 3 perpendiculars passing through midpoints

Source: Netherlands - Dutch NMO 1980 p3

January 28, 2023

concurrencyconcurrentgeometry

Problem Statement

Given is the non-right triangle

ABC

D,E

and

F

are the feet of the respective altitudes from

A,B

and

C

P,Q

and

R

are the respective midpoints of the line segments

EF

FD

and

DE

p \perp BC

passes through

P

q \perp CA

passes through

Q

and

r \perp AB

passes through

R

. Prove that the lines

p, q

and

r

pass through one point.