MathDB

equal angles starting with a fixed point on angle bisector

Source: 2006 ToT Spring Senior A P4

September 11, 2018

geometryequal anglesangle bisector

Problem Statement

In triangle

ABC

let

X

be some fixed point on bisector

AA'

while point

B'

be intersection of

BX

and

AC

and point

C'

be intersection of

CX

and

AB

. Let point

P

be intersection of segments

A'B'

and

CC'

while point

Q

be intersection of segments

A'C'

and

BB'

. Prove τhat

\angle PAC = \angle QAB