Question

O is a point in the interior of square ABCD such that OAB is an equilateral triangle. Show that triangle OCD is an isosceles triangle

Answer 1

abcd is a square
o is a point in the square such that triangle oab is equilateral triangle.
in a triangle diagonals are equal and bisect each other.
therefore, o is the point of bisection and intersection of diagonals.
therefore oc = od 
when triangle ocd is drawn,
it becomes an isosceles triangle since to of its sides are equal

hence proved

Answer 2

hope it helps you....