. triangle ABC, segments AD, BE, and CF are its altitudes, and H is its ortho-center. Circle ω, centered at O, passes through A and H and intersects sides AB and ACagain at Q and P (other than A), respectively.(a). triangle ABC, segments AD, BE, and CF are its altitudes, and H is its orthocenter. Circleω, centered at O, passes through A and H and intersects sides AB and AC again at Q and P (otherthan A), respectively.. I(C1) = C1, and I(ω) = ω. Let rayAO intersect ωA and ΩAat S and T , respectively. It is not difficult to see that AT > AS, because ωis tangent to ωA and ΩAexternally and internally,...