In the above figure, let be a right triangle, arcs and be segments of circles centered at and respectively, and define
(1)
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(2)
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(3)
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Then
(4)
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This can be seen by letting , , and and then solving the equations
(5)
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(6)
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(7)
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to obtain
(8)
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(9)
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(10)
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Plugging in the above gives
(11)
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by the Pythagorean theorem, so plugging in , the figure yields the algebraic identity
(12)
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The area of intersection formed (inside the triangle) by the circular sectors determined by arcs is given by
(13)
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