In an equilateral triangle `A B C` if `A D_|_B C` , then

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

If E is a point on side C A of an equilateral triangle A B C such that B E_|_C A , then A B^2+B C^2+C A^2= 2\ B E^2 (b) 3\ B E^2 (c) 4\ B E^2 (d) 6\ B E^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

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

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle. GIVEN : An equilateral triangle A B C such that A B=B C=C A=a . TO PROVE : a r(triangle A B C)=(sqrt(3))/4a^2 . CONSTRUCTION : Draw A D_|_B C .

In an equilateral triangle ABC, D is a point on side BC such that B D=1/3B C . Prove that 9A D^2=7A B^2 .

In Figure, A B C is an equilateral triangle. Find m\ /_B E C

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.