Ellipse by Paper Folding

Let be the center of a circle with radius and let be a point inside the circle. Choose a point on the circumference. Let be the intersection of the perpendicular bisector of and line . Then . So the point is on the ellipse with foci and and the sum of the distances from to the foci is .
To construct a tangent on the ellipse, fold the circle so that the circumference touches the point .

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