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concurrency wanted, 3 circles related, a perpendiculare bisector

Source: 2020 Greek TST p2

November 14, 2020

geometryconcurrencyconcurrent

Problem Statement

Given a triangle

ABC

inscribed in circle

c(O,R)

(with center

O

and radius

R

) with

AB<AC<BC

and let

BD

be a diameter of the circle

c

. The perpendicular bisector of

BD

intersects line

AC

at point

M

and line

AB

at point

N

. Line

ND

intersects the circle

c

at point

T

. Let

S

be the second intersection point of cicumcircles

c_1

of triangle

OCM

, and

c_2

of triangle

OAD

. Prove that lines

AD, CT

and

OS

pass through the same point.

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