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In 1725, he proved that if a polygon A1 A2… *An with an even number of sides is circumscribed about a circle, then A*1A2 + A3 A4 + A5 A6 + … = A2 A3 + A4 A5 +…. He also extended this theorem to polygons with an odd number of sides.
For a quadrilateral, the equality of the two tangents drawn from the same point readily shows that the sum of two opposite sides equals the semiperimeter of the quadrilateral: a + c = b + d.
Conics in a nutshell -------------------