Output
a b c = triangle a b c; o = circle o a b c; d = foot d a b c; e = foot e b a c; f = foot f c a b; h = orthocenter h a b c; m = on_line m d a, on_circle m o a; n = on_line n e b, on_circle n o a; p = on_line p f c, on_circle p o a ? cyclic c e h d