Find the radius the common circle of intersection and show that it is equal to \(\displaystyle \frac{r_1 r_2}{\sqrt{r_1^{2} + r_2^{2}}}\).

When two sphere intersect they form a circle if you join all the points of intersection, that is the common circle.

See this image, the silver portion is the common circle.

https://i.stack.imgur.com/fMCUK.jpg

When two sphere intersect they form a circle if you join all the points of intersection, that is the common circle.

See this image, the silver portion is the common circle.

https://i.stack.imgur.com/fMCUK.jpg

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