Let B and D be points on segments [AE] and [AF] respectively. Excircles of triangles ABF and ADE touching sides BF and DE is the same, and its center is I. BF and DE intersects at C. Let P1,P2,P3,P4,Q1,Q2,Q3,Q4 be the circumcenters of triangles IAB,IBC,ICD,IDA,IAE,IEC,ICF,IFA respectively.a) Show that points P1,P2,P3,P4 concylic and points Q1,Q2,Q3,Q4 concylic.
b) Denote centers of theese circles as O1 and O2. Prove that O1,O2 and I are collinear. geometrycircumcircletrigonometrygeometry proposed