What is the area between two circles, radius one, that go through each other's centres?Not sure if this requires calculus or not. I couldn't work it out. *

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- Nov 2nd 2009, 05:54 AMAquafinaArea between Circles
**What is the area between two circles, radius one, that go through each other's centres?**Not sure if this requires calculus or not. I couldn't work it out. *

- Nov 2nd 2009, 06:25 AMearboth
- Nov 2nd 2009, 07:45 AMAquafina
- Nov 2nd 2009, 10:50 AMukorov
referring to the attached pic:

both triangles ABC and DBC can be proved equilateral and congruent to each other.

the area of__sector__ABC

= (1/6)(pi)(1^2)

= pi/6

and the area of triangle ABC

= (1/2)(AB)(BC)(sin60)

= (1/2)(1)(1)(3^0.5 / 2)

= 3^0.5 / 4

the difference between these two areas is the area of each one red region (in attachment), let A be it.

hence, the total area of overlapped region of the two circles

= area of triangle ABC x 2 + 4A

= 3^0.5 /4 x 2 + 4(pi/6 - 3^0.5 / 4)

= 1.2284 sq. units - Nov 2nd 2009, 01:00 PMearboth