The two circles have the same centre. What’s the shaded area?
Solution 1
By adding a line passing through the centre of both circles, we have the following
Notice the line in green is composed of R + r, and the line in purple is composed of R -r.
Using the intersecting chord theorem, we have
where a, b, c and d are the line segments formed by the two intersecting lines in the circle.
In our question, we have
which equals
Notice the area of the shaded region is the difference between the two circles
Keep reading with a 7-day free trial
Subscribe to Mathematical Donuts 🍩 to keep reading this post and get 7 days of free access to the full post archives.