Enter the radius of two circles and the distance between their centers into the calculator to determine the area of intersection between the two circles.
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Area Between Two Intersecting Circles Formula
The following formula is used to calculate the area of intersection between two circles.
A = r_1^2 cos^{-1} \left( \frac{d^2 + r_1^2 - r_2^2}{2dr_1} \right) + r_2^2 cos^{-1} \left( \frac{d^2 + r_2^2 - r_1^2}{2dr_2} \right) - \frac{1}{2} \sqrt{(-d + r_1 + r_2)(d + r_1 - r_2)(d - r_1 + r_2)(d + r_1 + r_2)}Variables:
- A is the area of intersection
- r1 is the radius of the first circle
- r2 is the radius of the second circle
- d is the distance between the centers of the two circles
To calculate the area of intersection between two circles, use the formula above. This formula takes into account the radii of both circles and the distance between their centers to determine the overlapping area.
What is the Area Between Two Intersecting Circles?
The area between two intersecting circles, also known as the area of intersection, is the region that is common to both circles. This area can be calculated using the radii of the circles and the distance between their centers. The intersection area is significant in various fields such as geometry, physics, and engineering, where understanding the overlap between two circular regions is necessary.
How to Calculate the Area Between Two Intersecting Circles?
The following steps outline how to calculate the area of intersection between two circles.
- First, determine the radius of the first circle (r1).
- Next, determine the radius of the second circle (r2).
- Next, determine the distance between the centers of the two circles (d).
- Finally, use the formula to calculate the area of intersection.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Radius of Circle 1 (r1) = 5 m
Radius of Circle 2 (r2) = 7 m
Distance Between Centers (d) = 10 m