Triangle Arcs

In the above figure, let be a right triangle, arcs and be segments of circles centered at and respectively, and define

			(1)
			(2)
			(3)

Then

(4)

This can be seen by letting , , and and then solving the equations

			(5)
			(6)
			(7)

to obtain

			(8)
			(9)
			(10)

Plugging in the above gives

(11)

by the Pythagorean theorem, so plugging in , the figure yields the algebraic identity

(12)

The area of intersection formed (inside the triangle) by the circular sectors determined by arcs is given by

(13)