# Bernoulli's Lemniscate Formed from an Isosceles Trapezoid

Bernoulli's Lemniscate Formed from an Isosceles Trapezoid

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.

ABCD

ABCD

σ

G

H

AB

DC

G

H