Triangle ABC is a right triangle in a semicircle with AC as a diameter. Semicircles are also drawn with legs AB and BC as diameters.
If AB=12 and BC = 5, What is the sum of the shaded areas? Please see the attached diagram.
Solution. Since AB=12 and BC = 5, we have AC=13 (since AC^2=AB^2+BC^2)
The area S1 of semicircle with diameter AB=12 is ...
When the sides of a triangle are all diameters of semicircles, the area of a shaded region is found.