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1 How do you construct a regular polygon inside of a circle?

User Oleg Pasko
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Answer:

Step-by-step explanation:Draw a straight line using the protractor. This will be the center line of your circle (dividing it into semi-circles).Align the protractor so that both 0° and 180° lie on the center line. Mark the center point.Trace the semicircle along the protractor from 0 ° to 180°.

Put the protractor on the other side of the center line, again with both the 0°and 180° marks on the center line.[1]Complete the circle by tracing along the protractor.

Calculate the angle between adjacent vertices, α. Since a circle has 360°, divide 360° by n, the number of vertices (or sides) to get α.[2]

α=360°/n

α is the measured angle between lines drawn from the center of the circle to adjacent vertices.

For a dodecagon, n=12. A dodecagon has 12 sides and 12 vertices, so 360° divided by 12 is 30°, and α=30°.

Mark a point for each of the successive angles. Using the protractor, mark on the circumference of the circle all the multiples of angle α calculated above.[3]

Join the points marked on the circle with a line segment.[4] For a dodecagon there should be 12 marks and 12 sides, because it has 12 vertices. Don’t overlap the line segments.

If your points are outside of the circle, then simply mark another point along the radial line from the center onto the circle for each point and then join them.

Check to see that the sides are the same length. If they are, you can erase the circumscribed circle.Finished.

User Ahjmorton
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