Thread: Area 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. *

Originally Posted by Aquafina

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. *

One quarter of the area in question is the difference between a sector (radius = 1, central angle = 60°) and a right triangle. (see attachment)

Originally Posted by earboth

One quarter of the area in question is the difference between a sector (radius = 1, central angle = 60°) and a right triangle. (see attachment)

Don't you mean the Area of the triangle + the sector?

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

Originally Posted by Aquafina

Don't you mean the Area of the triangle + the sector?<<<<< No

1. The area of the sector (That's the area with the blue borderline) is



2. The area of the right triangle (That's the lightgrey area) is



3. The white area is



4. The area in question is