Find-the-area-intersected-by-three-circles-of-radius-1-centered-at-the-origin-at-1-0-and-1-1-respectively-

Question Number 210917 by depressiveshrek last updated on 22/Aug/24

Find the area intersected by three

circles of radius 1, centered at the

origin, at (1, 0) and (1, 1) respectively .

Answered by mr W last updated on 22/Aug/24

Commented by mr W last updated on 22/Aug/24

o n e s e c t o r w i t h a n g l e 30 ° :

A_{1} = \frac{30}{360} \times π \times 1^{2} = \frac{π}{12}

t w o s e g m e n t s w i t h a n g l e 60 ° :

A_{2} = 2 \times \frac{1^{2}}{2} \times (\frac{π}{3} - \sin 60 °) = \frac{π}{3} - \frac{\sqrt{3}}{2}

t o t a l s h a d e d a r e a :

\frac{π}{12} + \frac{π}{3} - \frac{\sqrt{3}}{2} = \frac{5 π - 6 \sqrt{3}}{12} \approx 0.443 ✓

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