Let the incircle of triangle ABC touch sides BC,CA and AB at D,E and F, respectively. Let ω,ω1,ω2 and ω3 denote the circumcircles of triangle ABC,AEF,BDF and CDE respectively.
Let ω and ω1 intersect at A and P,ω and ω2 intersect at B and Q,ω and ω3 intersect at C and R.
a. Prove that ω1,ω2 and ω3 intersect in a common point.
b. Show that PD,QE and RF are concurrent. geometrycircumcirclegeometric transformationhomothetysymmetrycyclic quadrilateralHi