Show that the altitudes of a triangle are concurrent

Prove that the altitudes of a triangle are concurrent.

Assuming the validity of the statement that the internal bisectors of the angles of a triangle are concurrent, prove that the altitudes of a triangle are concurrent.

Prove analytically that the altitudes of a triangle are concurrent.

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

Prove analytically : The altitudes of a triangle are concurrent.

Prove by vector method that the medians of a triangle are concurrent.

Show that the angle bisectors of a triangle are concurrent.