To construct a 19-gon, draw a circle with 2 (two) perpendicular diameters. From the point labelled D, construct an arc with the same radius intersecting the first circle in two points. Construt the midpoints of two radiuses (or radii) shown here as the bottom and right radii. Construct a line segment from point E to the midpoint as shown. Construct the perpendicular line to that line going through the other midpoint as shown. Where it intersects the outer circle, put a point. Call it X (not shown). Use your compass to mark off two lengths of X to line segment CD. Use those two lengths together to make your radius for the small circles (shown). Mark off 19 circles around the large circle, and connect the points accordingly (not shown).

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