<Dd> h c = p q (\ displaystyle h_ (c) = (\ sqrt (pq))) (Geometric mean theorem) </Dd> <P> For acute and right triangles the feet of the altitudes all fall on the triangle's sides (not extended). In an obtuse triangle (one with an obtuse angle), the foot of the altitude to the obtuse - angled vertex falls in the interior of the opposite side, but the feet of the altitudes to the acute - angled vertices fall on the opposite extended side, exterior to the triangle . This is illustrated in the adjacent diagram: in this obtuse triangle, an altitude dropped perpendicularly from the top vertex, which has an acute angle, intersects the extended horizontal side outside the triangle . </P> <P> The three (possibly extended) altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by H. The orthocenter lies inside the triangle if and only if the triangle is acute (i.e. does not have an angle greater than or equal to a right angle). If one angle is a right angle, the orthocenter coincides with the vertex at the right angle . </P> <P> Let A, B, C denote the vertices and also the angles of the triangle, and let a = BC, b = CA, c = AB be the side lengths . The orthocenter has trilinear coordinates </P>

Where do the altitudes of a triangle intersect