Bernoulli's Lemniscate Formed from an Isosceles Trapezoid

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Let be an isosceles trapezoid with horizontal bases. has an inscribed circle if the altitude of the trapezoid equals the geometric mean of the bases. Let and be the intersections of the circles with diameters and . Then the points and lie on a Bernoulli lemniscate.

Contributed by: Marko Razpet and Izidor Hafner (July 2018)
Open content licensed under CC BY-NC-SA


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