The median AM is drawn in the acute-angled triangle ABC with different sides. Its extension intersects the circumscribed circle w of this triangle at the point P. Let AH1 be the altitude ΔABC, H be the point of intersection of its altitudes. The rays MH and PH1 intersect the circle w at the points K and T, respectively. Prove that the circumscribed circle of ΔKTH1 touches the segment BC. (Hilko Danilo) geometrycircumcircletangentorthocenter