1. Geometry

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

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

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 $\displaystyle \Gamma$ in this problem?

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

Tonio

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

Tonio