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

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

Prove that the internal bisector of the angle A of a triangle ABC divides BC in the ratio AB:AC

Prove using vectors: Medians of a triangle are concurrent.

Prove that the bisectors of the angles of a linear pair are at right angle.

Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one-half of the vertical angle.

Prove that the angle between internal bisector of one base angle and the external bisector of the other base angle of a triangle is equal to one half of the vertical angle.

Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

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).