Notes
circles around a triangle solution
Circles Around a Triangle
The diameters of these circles form a triangle. What’s the total shaded area?
With the regions labelled as above, they combine as follows:
- and are large semi-circles, write this as
- and are medium semi-circles, write this as
- and are small semi-circles, write this as
- is the triangle, write this as
Then the shaded region can be expressed as follows:
As the triangle has side lengths , , and it is a right-angled triangle and has area . So the shaded regions have total area .
Created on September 25, 2021 21:35:13
by
Andrew Stacey