In any triangle ABC, if the angle bisector of `/_A`and perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC

In any triangle ABC, if the angle bisector of /_A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

Prove that If the bisector of any angle of a triangle and the perpendicular bisector of its opposite side intersect, they will intersect on the circumcircle of the triangle.

The vertices A, B, C of a triangle ABC have co-ordinates (4,4), (5,3) and (6,0) respectively. Find the equations of the perpendicular bisectors of AB and BC, the coordinates of the circumcentre and the radius of the circumcircle of the triangle ABC.

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.

If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F. Prove that : F is equidistant from AB and AC.

In an acute angled triangle ABC , let AD, BE and CF be the perpendicular opposite sides of the triangle. The ratio of the product of the side lengths of the triangles DEF and ABC , is equal to

In triangle ABC,the bisector of interior angle A and the bisector angle C meet at point O. Prove that angle AOC=(1)/(2)angleB

In a triangle, with usual notations, the length of the bisector of angle A is