MathDB

Consider an acute-angled triangle

ABC

with

AB<AC

and let

\omega

be its circumscribed circle. Let

t_B

and

t_C

be the tangents to the circle

\omega

at points

B

and

C

, respectively, and let

L

be their intersection. The straight line passing through the point

B

and parallel to

AC

intersects

t_C

in point

D

. The straight line passing through the point

C

and parallel to

AB

intersects

t_B

in point

E

. The circumcircle of the triangle

BDC

intersects

AC

T

, where

T

is located between

A

and

C

. The circumcircle of the triangle

BEC

intersects the line

AB

(or its extension) in

S

, where

B

is located between

S

and

A

. Prove that

ST

AL

, and

BC

are concurrent.

\text{Vangelis Psychas and Silouanos Brazitikos}

Problem Statement