6 Con s t r u c t i on o f a r e gu l a r h e p t agon Construct a heptagon, given one side To construct a regular heptagon, given the length of one of its sides, follow these steps: Construct a heptagon, given the circumscribed circle To construct a regular heptagon, given the radius of the circumscribed circle, follow these steps: Step 1. From vertex A, draw an angle of 30º. Step 2. From B, draw a perpendicular line to AB. Where it intersects the 30º angle line, we obtain point N. Step 3. Use centre A and radius AN. Draw an arc. Step 4. Draw the perpendicular bisector of AB. At the point of intersection with the arc in step 3, we get point O. This is the centre of the circumscribed circumference of the heptagon. Step 5. Use centre O and radius OA. Draw the circumscribed circumference. Step 6. To complete the drawing, copy the length of AB consecutively around the circumference. Step 1. Draw the perpendicular diameters of the circumference, AB and CD. Step 2. Draw the perpendicular bisector of one of the radii. For example, use OD. This obtains point M. Extend the bisector to obtain point N. Step 3. The segment MN is the length of the side of the regular heptagon. From vertex A, translate this segment consecutively around the circumference. A A A A B A A B B B B B N N N N N O O O 30º A A A B B O M M N N B C C C D D D
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