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.

The angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

A triangle ABC is right angled at A. AM is drawn perpendicular to BC. Prove that angleBAM=angleACB

Prove that the perpendicular bisectors of the sides of triangle are concurrent.

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

Draw a right angled triangle .Construct three perpendicular bisector on each of its sides .Where do the three bisectors meet .

In triangleABC , AD is the perpendicular bisector of BC. Show that triangleABC is an isosceles triangle in which AB=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

ABC is a triangle in which angleBAc = 30^@ . Prove that BC is the radius of the circumcircle of triangleABC , whose centre O.

In DeltaABC , AD is the perpendicular bisector of BC (See Fig. ). Show that DeltaABC is an isosceles triangle in which AB = AC.

In DeltaABC , AD is the perpendicular bisector of BC (See Fig. ). Show that DeltaABC is an isosceles triangle in which AB = AC.