Chi. TST 2016 Q6 (day 2)

For discussing Olympiad level Geometry Problems
User avatar
Kazi_Zareer
Posts:86
Joined:Thu Aug 20, 2015 7:11 pm
Location:Malibagh,Dhaka-1217
Chi. TST 2016 Q6 (day 2)

Unread post by Kazi_Zareer » Fri May 27, 2016 2:44 am

The diagonals of a cyclic quadrilateral $ABCD$ intersect at $P$, and there exist a circle $\Gamma$ tangent to the extensions of $AB,BC,AD,DC$ at $X,Y,Z,T$ respectively. Circle $\Omega$ passes through points $A,B$, and is externally tangent to circle $\Gamma$ at $S$. Prove that $SP\perp ST$.
We cannot solve our problems with the same thinking we used when we create them.

Post Reply