`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` .

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 .

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 fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

A B C is a triangle in which /_B =2 /_CdotD is a point on B C such that A D bisects /_B A C and A B=C D . Prove that /_B A C=72^0dot

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

A B C is a triangle in which /_B=2/_C. D is a point on B C such that A D bisects /_B A C\ a n d\ A B=C D . Prove that /_B A C=72^@ .

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

In Figure, A B C is a triangle in which /_B=2/_C . D is a point on side B C such that A D bisects /_B A C\ a n d\ A B=C D. B P is the bisector of /_B . The measure of /_B A C is (a) 72^0 (b) 73^0 (c) 74^0 (d) 96^0

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