(Solved): Alhazen's Moons Alhazen was a prominent Arab mathematician, astronomer, and physicist of the Islam ...

Alhazen's Moons Alhazen was a prominent Arab mathematician, astronomer, and physicist of the Islamic Golden Age, who built on many elementary geometry problems from Euclid. One of his creations was Alhazen's two moons, built on the right-angled triangle AABC as shown below. The outer boundaries of the two moons are semicircles of diameters equal to the altitude and the base of AABC respectively, while their inner boundaries are formed by the circumcircle of AABC. & C B 1. Establish a polar coordinate system with the origin at vertex B and find the polar equation of the circumcircle centred at the intersection of the three right-bisectors of the edges of AABC. By observation, the line y = -x is tangential to the circumcircle at B. 2. Choose an appropriate vector field and use the Green's Theorem to find the combined area of the two moons using polar coordinates. Comment on your results.