# Geometry

• July 16th 2010, 11:01 PM
simplependulum
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 . (Happy)

Moderator edit: Approved Challenge question.
• July 17th 2010, 11:23 AM
Chris11
Did you recieve the honourable mention for this year's IMO?
• July 17th 2010, 04:19 PM
chiph588@
Quote:

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 . (Happy)

May be a dumb question, but what exactly is $\Gamma$ in this problem?
• July 17th 2010, 07:43 PM
tonio
Quote:

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
• July 17th 2010, 08:46 PM
chiph588@
Quote:

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

Tonio