2007 JBMO Problems/Problem 2
Let I be the intersection between and the angle bisector of
So
So
We can conclude that
are on a same circle.
So
Because
and
we have
So
So
is on the angle bisector of
and on the mediator of
.
The first posibility is that
i steh south pole of
so
is on the circle of
but we can easily seen that not possible
The second possibility is that
is isosceles in
. So because
and
is isosceles in
we have
. So