To construct a regular 17-gon:

Construct a circle, a diameter, and a radius perpendicular to the diameter.

Trisect one half of the diameter as shown.

Draw a diagonal line from the end of the diameter to the end of the radius as shown, forming a 45°, 45°, 90° triangle and bisect it.

Draw a ray as shown.

Using where the ray intersects the circle to the endpoint of the radius of the big circle as radius, mark off 17 congruent circles and connect their centers (connections are not shown) to form a regular 17-gon.

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