The brilliant plumage of what national bird of india is due to an optical interference phenomenon called the bragg reflection?

The correct answer is the peacock. The plumage found in Indian peacocks are because of the Bragg reflection phenomenon.

I'm pretty sure there's a geometry rule for   anyways, if the triangle is equilateral, and the circle is circumscribed, the circle is outside of the triangle.  to find the area, you need the radius.  the radius should be a straight line from the center of the triangle to any of it's points.  draw lines from the center of the circle to each of the triangle points.  draw three more lines from the center to the middle of the sides of the triangle.  you should now have six separate 30-60-90 triangles inside of your original triangle. use your 30-60-90 rules to solve for the radius, then the circumference. 

It is useful for historians to write narratives so that history can be passed on from their point of view.  think about a story being told in third person, then think about it again being told in first person, by someone who actually experienced the event.