I am stumped on how to solve this problem. I've tried to look up the problem, but to no avail. What I need to know is how can I find the area of a semicircle cut off by the curve of another semicircle?
I have an example image here
The radius of the larger semicircle is 1 inch, while the radius of the smaller semicircle is 0.5 inches. I can easily understand how to find the area of the larger semicircle, but I cannot find the area of the smaller one, as it is not a true semicircle (the bottom is cut off by the curve of the larger semicircle.)
Any help or an answer would be appreciated, thanks.
Best Answer
N.B. $\operatorname{cs}(ACD)$ is the circle segment defined by the rays, $AC$ and $AD$.
In the piture below, we have that $$\operatorname{cs}(ACD)+\operatorname{cs}(BCD)$$ contains the part were looking for. However we have overcounted. Can you see by how much we overcounted (i.e. what we now need to substract)?