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Let $ABC$ be an acute-angled triangle with $AB < AC$ ...

Source:

August 8, 2015

geometrycircumcircle

Problem Statement

Let

ABC

be an acute-angled triangle with

AB < AC

, and let points

D

and

E

be chosen on the side

AC

and

BC

respectively in such a way that

AD = AE = AB

. The circumcircle of

ABE

intersects the line

AC

A

and

F

and the line

DE

E

and

P

. Prove that

P

is the circumcentre of

BDF