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Diameter of an intersection?

Question

Two overlapping spherical soap bubbles, whose centers are 50 mm apart, have radii 40 mm and 30 mm. What is the diameter D of their circle of intersection?

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2 answers to this question

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In a plane containing the centers, one sees a 30 40 50 triangle.
The radius of intersection is perpendicular to the 50 side.
Thus,

30x40 = 50xr.

d = 2r = 48.

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