Circumcenter. why is the orthocenter of a right triangle on the vertex that is a right angle? – Kevin Aug 17 '12 at 18:34. Find the slopes of the altitudes for those two sides. So, let us learn how to construct altitudes of a triangle. For an obtuse triangle, it lies outside of the triangle. Solve the corresponding x and y values, giving you the coordinates of the orthocenter. Find the equations of two line segments forming sides of the triangle. When the position of an Orthocenter of a triangle is given, If the Orthocenter of a triangle lies in the center of a triangle then the triangle is an acute triangle. And then I find the orthocenter of each one: It appears that all acute triangles have the orthocenter inside the triangle. The orthocenter of a triangle is the intersection of the triangle's three altitudes. The altitude of the third angle, the one opposite the hypotenuse, runs through the same intersection point. Since two of the sides of a right triangle already sit at right angles to one another, the orthocenter of the right triangle is where those two sides intersect the form a right angle. Let ABC be the triangle AD,BE and CF are three altitudes from A, B and C to BC, CA and AB respectively. If I had a computer I would have drawn some figures also. It lies inside for an acute and outside for an obtuse triangle. Consider the points of the sides to be x1,y1 and x2,y2 respectively. 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