in a triangle ABC and R is the radius of the circle into which the triangle is inscribed(in other words it is the circum radius of the triangle)
then prove it is an equilateral triangle
It took me quite a while to see how to simplify the left hand side to get . (It's correct, but I'll leave it to sa-ri-ga-ma to provide the details. )
So we know that . Multiply out the left side to get . Thus the equation becomes , which you can write as . That obviously only holds if .