# Ellipse by Paper Folding

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 .

G

r

A

B

C

AB

GB

AC+CG=BG=r

C

A

G

C

r

To construct a tangent on the ellipse, fold the circle so that the circumference touches the point .

A