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Let ABC be an acute triangle with orthocenter H, and let W be a point on the side BC, between B and C. The points M and N are the feet of the altitudes drawn from B and C, respectively. is the circumcircle of triangle BWN, and X is a point such that WX is a diameter of . Similarly, is the circumcircle of triangle CWM, and Y is a point such that WY is a diameter of . Show that the points X, Y, and H are collinear.
(point A 151 84)
(point B 92 260)
(point C 310 258)
(segment d1 A B)
(line d2 B C)
(segment d3 C A)
(projection N C d1)
Let ABC be a triangle, and a=length(BC), b=length(CA) and c=length(AB).Let
Then area S of the triangle is
We know that
so we have