Question 118
A right triangle isosceles $A B C$, with the right angle at $C$, and the legs of length $2$. An arc of circle $l$ with center $A$ divides the triangle into two parts of the same area, while the arc of circle $m$ with center at $B$ is tangent to the arc $l$ at a point of the hypotenuse $A B$. Find the area of the portion of the triangle not covered by the circular sectors corresponding to the two arcs.