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The distance between the centers of two circles K1 and K2 is 2cm. They intersect under a right angle, the radius of K1 is 1cm. Determine the surface area of the figure that belongs to both circles.

[This is a little sketch.[1]

So I drew it like this. It is obvious that the radius of K2 is then the square root of 3. I have no idea how to get the surface area of this weird shape. Any tips?

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  • $\begingroup$ By "surface area", do you mean perimeter or area within the shape? $\endgroup$ – Benedict Randall Shaw Oct 24 '18 at 22:14
  • $\begingroup$ @BenedictRandallShaw area within the shape that is the union of both circles. $\endgroup$ – RiktasMath Oct 24 '18 at 22:16
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You can calculate the area of a circular cap as shown below. Two such circular caps produce your 'weird shape'. enter image description here

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  • $\begingroup$ This doesn't look anything like the shape I am supposed to get? $\endgroup$ – RiktasMath Oct 24 '18 at 22:18
  • $\begingroup$ If you draw a vertical line between the two points of intersection of your two circles, you will see that this divides your shape into two such caps...attached back-to-back $\endgroup$ – Penguino Oct 24 '18 at 22:20
  • $\begingroup$ I did it! Thanks for the help!!! $\endgroup$ – RiktasMath Oct 24 '18 at 22:41

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