WOLFRAM|DEMONSTRATIONS PROJECT

Bernoulli's Lemniscate Formed from an Isosceles Trapezoid

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