Why is it 5 : 30 p. m in india and 12 : 00 noon in london ?

Because after the sun is 'overhead' in India, it takes roughly 5-1/2 hours
for the Earth to turn far enough to place the sun 'overhead' in London.
Our clocks are built to match what the sun appears to do.

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.