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Concurrent lines

Source: Romania ,4th TST 2014,Problem 1

December 5, 2014

geometrycircumcircletrigonometryangle bisectorprojective geometrygeometry proposed

Problem Statement

Let

\triangle ABC

be an acute triangle of circumcentre

O

. Let the tangents to the circumcircle of

\triangle ABC

in points

B

and

C

meet at point

P

. The circle of centre

P

and radius

PB=PC

meets the internal angle bisector of

\angle BAC

inside

\triangle ABC

at point

S

, and

OS \cap BC = D

. The projections of

S

on

AC

and

AB

respectively are

E

and

F

. Prove that

AD

,

BE

and

CF

are concurrent.
Author: Cosmin Pohoata

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