Find the area intersected by three circles of radius 1, centered at the origin, at (1, 0) and (1, 1) respectively.


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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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