1. ## Geometry

Let $P$ be a point inside the triangle $ABC$ . The lines $AP , BP$ and $CP$ intersect the circumcircle $\Gamma$ of triangle $ABC$ agian at the points $K,L$ and $M$ respectively . The tagent to $\Gamma$ at $C$ intersects the line $AB$ at $S$ . Suppose that $SC = SP$ . Prove that $MK=ML$ .

If you could answer this problem , you are able to receive the Honourable Mention of this year IMO .

Moderator edit: Approved Challenge question.

2. Did you recieve the honourable mention for this year's IMO?

3. Originally Posted by simplependulum
Let $P$ be a point inside the triangle $ABC$ . The lines $AP , BP$ and $CP$ intersect the circumcircle $\Gamma$ of triangle $ABC$ agian at the points $K,L$ and $M$ respectively . The tagent to $\Gamma$ at $C$ intersects the line $AB$ at $S$ . Suppose that $SC = SP$ . Prove that $MK=ML$ .

If you could answer this problem , you are able to receive the Honourable Mention of this year IMO .
May be a dumb question, but what exactly is $\Gamma$ in this problem?

4. Originally Posted by chiph588@
May be a dumb question, but what exactly is $\Gamma$ in this problem?
$\Gamma$ is the circumcircle = the unique circle passing through all the three vertices of the triangle.

Tonio

5. Originally Posted by tonio
$\Gamma$ is the circumcircle = the unique circle passing through all the three vertices of the triangle.

Tonio