Prove analytically that the altitudes of a triangle are concurrent.

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

The co-ordinates of points A, B and C are (1, 2),(-2, 1) and (0, 6) respectively. Verify that the medians of the triangle ABC are concurrent. Also, find the co-ordinates of the point of concurrence (centroid).

How many altitudes can a triangle have?

Show, by vector method, that the angular bisector of a triangle are concurrent and find its expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.

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

Using vectors, show that the medians of a triangle are concurrent.

Altitudes of a triangle always lie in its exterior.

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