Show that the perpendicular bisectors of the sides of a triangle are concurrent.

Show that the perpendicular bisectors of the sides of the triangle with vertices (7, 2), (5, -2) and (-1, 0) are concurrent. Also find the coordinates of the point of concurrence (circumcentre).

Prove that the internal bisectors of the angles of a triangle are concurrent

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

Prove that the altitudes of a triangle are concurrent.

Show that the altitudes of a triangle are concurrent

Prove that the medians of a triangle are concurrent.

The perpendicular bisectors of the sides of a triangle ABC meet at I. Prove that : IA = IB = IC.

Prove using vectors: Medians of a triangle are concurrent.

Show, by vector methods, that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.

The equations of the perpendicular bisectors of the sides A Ba n dA C of triangle A B C are x-y+5=0 and x+2y=0 , respectively. If the point A is (1,-2) , then find the equation of the line B Cdot