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Angle Bisector Intersects Circumcircle

Source: 2012 IrMO Paper 2 Problem 2

February 16, 2018

geometryangle bisectorcircumcircle

Problem Statement

Consider a triangle

ABC

with

|AB|\neq |AC|

. The angle bisector of the angle

CAB

intersects the circumcircle of

\triangle ABC

at two points

A

and

D

. The circle of center

D

and radius

B

intersects the line

AC

at two points

C

and

B’

. The line

BB’

intersects the circumcircle of

\triangle ABC

at

B

and

E

. Prove that

B’

is the orthocenter of

\triangle AED

.

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