In an equilateral triangle `A B C` if `A D_|_B C ,` then `A D^2` = (a)`C D^2` (b) `2C D^2` (c) `3C D^2` (d) `4C D^2`

If A B C is an equilateral triangle such that A D_|_B C , then A D^2= (a) 3/2D C^2 (b) 2\ D C^2 (c) 3\ C D^2 (d) 4\ D C^2

In an equilateral triangle A B C , if A D_|_B C , then (a) 2\ A B^2=3\ A D^2 (b) 4\ A B^2=3\ A D^2 (c) 3\ A B^2=4\ A D^2 (d) 3\ A B^2=2\ A D^2

In an equilateral A B C , A D_|_B C , prove that A D^2=3\ B D^2

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

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

A point D is on the side B C of an equilateral triangle A B C such that D C=1/4\ B C . Prove that A D^2=13\ C D^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

In a triangle A B C ,\ \ A D_|_B C and A D^2=B DxxC Ddot Prove that A B C is a right triangle.