MathDB

BP=PQ wanted, CD=CE, right isosceles (2021 Novosibirsk Oral Geo Oly 8.5)

Source:

May 24, 2021

geometryright triangleisoscelesequal segments

Problem Statement

On the legs

AC

and

BC

of an isosceles right-angled triangle with a right angle

C

, points

D

and

E

are taken, respectively, so that

CD = CE

. Perpendiculars on line

AE

from points

C

and

D

intersect segment

AB

at points

P

and

Q

, respectively. Prove that

BP = PQ