In an isosceles triangle `A B C` with `A B=A C` , `B D` is perpendicular from `B` to the side `A C` . Prove that `B D^2-C D^2=2\ C D A D`

In an isosceles triangle A B C with A B=A C and B D_|_A Cdot Prove that B D^2-C D^2=2C DdotA Ddot

In Figure, A B C is an isosceles triangle with A B=A C ,\ B D\ a n d\ C E are two medians of the triangle. Prove that B D=C E

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

\ ABC is an isosceles triangle with A B=A C . Side B A is produced to D such that A B=A D . Prove that /_B C D is a right angle.

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CXC D . Prove that B D=B C .

If A B C is an isosceles triangle with A B=A Cdot Prove that the perpendiculars from the vertices B\ a n d\ C to their opposite sides are equal.

A B C is an isosceles triangle with A B=A C and D is a point on A C such that B C^2=A CxC Ddot Prove that B D=B C

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C* D E+1/4B C^2

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 .