Prove that the perpendicular from the vertices to the opposite sides (i.e. Altitudes) of a triangle concurrent.

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

Prove analytically that the altitudes of a triangle are concurrent.

Prove that the perpendicular bisectors of the sides of triangle are concurrent.

If l_(1), l_(2), l_(3) are respectively the perpendicular from the vertices of a triangle on the opposite side, then show that l_(1)l_(2) l_(3) =(a^(2)b ^(2) c^(2))/(8R^(3)).

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

Prove that the median from the vertex of an isosceles triangle is the bisector of the vertical angle.

Prove that the lines joining the vertices of a tetrahedron to the centroids of the opposite faces are concurrent.

Prove analytically that the : medians of a triangle are concurrent.

Write the : Angle opposite to the side LM of triangle LMN

In an acute angle Delta ABC, let AD, BE and CF be the perpendicular from A, B and C upon the opposite sides of the triangle. (All symbols used have usual meaning in a tiangle.) The orthocentre of the Delta ABC, is the