let-s-say-there-are-two-circles-with-their-centers-A1-and-A2-and-their-radii-are-equal-to-r1-and-r2-let-n-be-the-distance-between-the-centers-of-the-two-circles-and-n-r1-r2-Is-there-a-way-to-find-h

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Question Number 215774 by Engr_Jidda last updated on 17/Jan/25

let's say there are two circles with their centers A1 and A2 and their radii are equal to r1 and r2 ,let n be the distance between the centers of the two circles and n<r1+r2. Is there a way to find how much is the area that is formed when the two circles are overlapping ?

Answered by AntonCWX last updated on 18/Jan/25

Commented by AntonCWX last updated on 18/Jan/25

Both α and β are in radian Red Region Area =(r_1 )^2 (α−sin(((180α)/π))) Blue Region Area =(r_2 )^2 (β−sin(((180β)/π))) Total area =r_1 ^2 (α−sin(((180α)/π)))+r_2 ^2 (β−sin(((180β)/π)))

B o t h α a n d β a r e i n r a d i a n

R e d R e g i o n A r e a

= {(r_{1})}^{2} (α - s i n (\frac{180 α}{π}))

B l u e R e g i o n A r e a

= {(r_{2})}^{2} (β - s i n (\frac{180 β}{π}))

T o t a l a r e a

= r_{1}^{2} (α - s i n (\frac{180 α}{π})) + r_{2}^{2} (β - s i n (\frac{180 β}{π}))

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let-s-say-there-are-two-circles-with-their-centers-A1-and-A2-and-their-radii-are-equal-to-r1-and-r2-let-n-be-the-distance-between-the-centers-of-the-two-circles-and-n-r1-r2-Is-there-a-way-to-find-h

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