Let ABC be an acute, non isosceles with I is its incenter. Denote D,E as tangent points of (I) on AB,AC, respectively. The median segments respect to vertex A of triangles ABE and ACD meet(I) atP,Q, respectively. Take points M,N on the line DE such that AM⊥BE and AN⊥CD respectively.
a) Prove that A lies on the radical axis of (MIP) and (NIQ).
b) Suppose that the orthocenter H of triangle ABC lies on (I). Prove that there exists a line which is tangent to three circles of center A,B,C and all pass through H. geometrycirclesorthocenterperpendicularincenterAZE EGMO TST