In `Delta ABC, AB = AC. A` circle is drawn with diameter AB and it intersects BC at D. Prove that D is the midpoint of BC.

In a right angle triangle Delta ABC is which /_B=90^(@) a circle is drawn with AB diameter intersecting the hypotenuse AC at P.Prove that the tangent to the circle at PQ bisects BC.

Two circles are drawn with sides AB,AC of a triangle ABC as diameters.The circles intersect at a point D. Prove that D lies on BC.

Two circles are drawn with sides AB and AC of a triangle ABC as diameters

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.Given: A ABC in which AB=AC and a circle is drawn by taking AB as diameter which intersects the side BC of triangle at D To Prove: BD=DC Construction : Join AD

An isosceles triangle ABC, with AB = AC, circumscribes a circle, touching BC at P, AC at Q and AB at R. Prove that the contact point P bisects BC.

In an isosceles triangle ABC with AB=AC a circle passing through B and C intersects the sides AB and AC at D and E respectively. Prove that DE|CB.

Delta ABC is a right triangle right angled at A such that AB=AC and bisector of /_C intersects the side AB at D.Prove that AC+AD=BC .

ABC is a right triangle with AB = AC.If bisector of angle A meet BC at D then prove that BC =2 AD .

ABC is a triangle A line is drawn parallel to BC to meet AB and AC in D and E respectively. Prove that the median through A bisects DE.

In an isosceles triangle ABC with AB=AC , a circle passing through B and C intersects the sides AB and AC at D and E respectively.Prove that DEBC