Question 26
a) Leandro draws a lunula of Hippocrates as shown in the following figure: 
In this figure, the triangle $A B C$ is rectangle and isosceles. The lunula is the region in the form of a crescent moon internal to a semicircle and external to the other semicircle, as shown in the figure. The first has a radius equal to the length of the $A B$ side and the second has a radius equal to half the length of the hypotenuse $B C$. Show that the area of the Hippocratic Lunula drawn by Leandro is equal to the area of the right triangle $A B C$.
b) Inspired by Leandro's drawing, Renato decides to draw the lunulas of Alhazen, as shown in the figure below:
In this figure, the lunulas are the regions in the shape of a crescent moon. A right triangle $A B C$ and three semi-circumferences are used to obtain these regions. The length of the radius of the largest of the semi-circumferences is equal to half the length of the hypotenuse, while the two smaller ones have a radius equal to half the length of the corresponding side. Show that the sum of the areas of the two lunulas drawn by Renato is equal to the area of the triangle $A B C$.
In this figure, the triangle $A B C$ is rectangle and isosceles. The lunula is the region in the form of a crescent moon internal to a semicircle and external to the other semicircle, as shown in the figure. The first has a radius equal to the length of the $A B$ side and the second has a radius equal to half the length of the hypotenuse $B C$. Show that the area of the Hippocratic Lunula drawn by Leandro is equal to the area of the right triangle $A B C$. b) Inspired by Leandro's drawing, Renato decides to draw the lunulas of Alhazen, as shown in the figure below:
In this figure, the lunulas are the regions in the shape of a crescent moon. A right triangle $A B C$ and three semi-circumferences are used to obtain these regions. The length of the radius of the largest of the semi-circumferences is equal to half the length of the hypotenuse, while the two smaller ones have a radius equal to half the length of the corresponding side. Show that the sum of the areas of the two lunulas drawn by Renato is equal to the area of the triangle $A B C$.