Let ω be the circumcircle of acute triangle ABC where ∠A<∠B and M,N be the midpoints of minor arcs BC,AC of ω respectively. The line PC is parallel to MN, intersecting ω at P (different from C). Let I be the incentre of ABC and let PI intersect ω again at the point T.
1) Prove that MP⋅MT=NP⋅NT;
2) Let Q be an arbitrary point on minor arc AB and I,J be the incentres of triangles AQC,BCQ. Prove that Q,I,J,T are concyclic. geometrycircumcircleincentergeometry proposed