MathDB

angle chasing in a triangle 120-30-30

Source: 2012 Sharygin Geometry Olympiad Final Round 8.4

August 3, 2018

Angle Chasingisoscelesgeometry

Problem Statement

Let

ABC

be an isosceles triangle with

\angle B = 120^o

. Points

P

and

Q

are chosen on the prolongations of segments

AB

and

CB

beyond point

B

so that the rays

AQ

and

CP

intersect and are perpendicular to each other. Prove that

\angle PQB = 2\angle PCQ

.
(A.Akopyan, D.Shvetsov)