If K is a point on the side BC of an equilateral triangle ABC and if `/_BAK =15^@`, then the ratio of `(AK)/(AB)` is

If E is a point on side r:A of an equilateral triangle ABC such that BE bot CA , then prove that AB^(2) +BC^(2) +CA^(2) = 4BE^(2) .

If D, E and F are the mid-points of the sides of an equilateral triangle ABC, then the ratio of the area of triangle DEF and DCF is :

If E is a point on side CA of an equilateral triangle ABC such that BE bot CA , then AB^2 + BC^2 + CA^2 is equal to___

A point D is on the side BC of an equilateral triangle ABC such that DC=(1)/(4)BC. Prove that AD^(2)=13CD^(2)

D,E and F are respectively the mid points of the sides BC,CA and AB of an equilateral triangle ABC, prove that DEF is also equilateral triangle.

If D,E and F are respectively the midpoints of the sides BC,CA and AB of an equilateral triangle ABC ,prove that /_DEF is also an equilateral triangle.