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concurrency wanted, 2 circles and tangents related

Source: Balkan MO Shortlist 2013 G4 BMO

March 3, 2020

geometrycirclesconcurrencyconcurrent

Problem Statement

Let

c(O, R)

be a circle,

AB

a diameter and

C

an arbitrary point on the circle different than

A

and

B

such that

\angle AOC > 90^o

. On the radius

OC

we consider point

K

and the circle

c_1(K, KC)

. The extension of the segment

KB

meets the circle

(c)

at point

E

. From

E

we consider the tangents

ES

and

ET

to the circle

(c_1)

. Prove that the lines

BE, ST

and

AC

are concurrent.

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