Let ABC be a triangle with O the circumcenter and I the incenter. Let D,E and F be the tangent points of the inscripted circle with AB, BC and AC.

1. Prove that orthocenter of DEF lies on the line IO

2. Prove that the distance of D, E and F from IO are three numbers where the biggest among the three is equal to the sum of the other two.

I thinks that some property about points circle could help, but can't figure out how!...