Problem 2.
Let

be an acute-angled triangle with
. Let

be the circumcircle of
. Let

be the midpoint of the arc

of

containing
. The perpendicular from

to

meets

at

and meets

again at
. The line through

parallel to

meets line

at
. Denote the circumcircle of triangle

by
. Let

meet

again at
. Prove that the line tangent to

at

meets line

on the internal angle bisector of
.
proposed by Tiago MourĂ£o and
Nuno Arala, Colombia