MathDB

# wanted, 3 right isosceles on sides of ABC (2013 NZOMC Camp Sel. p9)

Source:

January 4, 2021

parallelogramgeometryright triangleisosceles

Problem Statement

Let

ABC

be a triangle with

\angle CAB > 45^o

and

\angle CBA > 45^o

. Construct an isosceles right angled triangle

RAB

with

AB

as its hypotenuse and

R

inside

ABC

. Also construct isosceles right angled triangles

ACQ

and

BCP

having

AC

and

BC

respectively as their hypotenuses and lying entirely outside

ABC

. Show that

CQRP

is a parallelogram.