Question

Given (x y) coordinates of two circles and their radii find area of intersection c++

Answer 1

Answer:

Label the center of the first circle $C$ and the center of the second circle $C'$. Label one of the points of intersection of the two circles $A$ and the other $B$. Let the radius of the circles be $r>0$. It should be clear that the following lengths are all equal to $r$. $AC$, $AC'$, $BC$, $BC'$, $CC'$. With a simple application of Pythagoras' Theorem, we get that the length of the line segment $AB [/tex[ is [tex] \sqrt{3}r$

With some basic trigonometry, we find the angles $\angle ACB$=$\angle AC'B$=$\dfrac{2\pi}{3}$. So, the area of one half of the intersection is the area of a circular segment with angle $\theta=\dfrac{2\pi}{3}$ and radius $r$, which gives an area of $\dfrac{r^2}{2}(\theta-\sin\theta)$=$\dfrac{r^2}{2}\left(\dfrac{2\pi}{3}-\dfrac{\sqrt{3}}{2}\right)$ and so the area of the entire intersection is twice this. This gives an area of $r^2\left(\dfrac{2\pi}{3}-\dfrac{\sqrt{3}}{2}\right).$

Answer 2

Answer:

Here is your answer ll

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