Two circles are drawn with sides `A B ,A C` of a triangle `A B C` as diameters. The circles intersect at a point `D`. Prove that `D` lies on `B C`.

Two circles are drawn with sides A B ,A C of a triangle A B C as diameters. The circles intersect at a point Ddot Prove that D lies on B Cdot

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side

If circles are drawn taking two sides of a triangle as diameters, prove that the point ofintersection of these circles lie on the third side

In an equilateral triangle A B C the side B C is trisected at D . Prove that 9\ A D^2=7\ A B^2

The perpendicular A D on the base B C of a triangle A B C intersects B C at D so that D B=3C D . Prove that 2\ A B^2=2\ A C^2+B C^2 .

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

Two circle intersect in A and B and AC and AD are respectively the diameters of the circles. Prove that C , B , D are collinear.

Two circle with centres A and B intersect at C and Ddot Prove that /_A C B=/_A D Bdot

D and E are points on equal sides A B and A C of an isosceles triangle A B C such that A D=A E . Prove that B ,C ,D ,E are concylic.

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .