MathDB

P, Q, R, S lie either on a circle or on one straight line

Source: Germany Federal - Bundeswettbewerb Mathematik 2010, round 2, p3

April 14, 2020

Concycliccollinearprojectionsaltitudeperpendiculargeometry

Problem Statement

Given an acute-angled triangle

ABC

. Let

CB

be the altitude and

E

a random point on the line

CD

. Finally, let

P, Q, R

and

S

are the projections of

D

on the straight lines

AC, AE, BE

and

BC

. Prove that the points

P, Q, R

and

S

lie either on a circle or on one straight line.