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.

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

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.

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.

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

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 ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that : AD = CE.

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

In a triangle ABC , AB = AC and angle A = 36^(@) If the internal bisector of angle C meets AB at D . Prove that AD = BC.

In a triangle, ABC, the equation of the perpendicular bisector of AC is 3x - 2y + 8 = 0 . If the coordinates of the points A and B are (1, -1) & (3, 1) respectively, then the equation of the line BC & the centre of the circum-circle of the triangle ABC will be