Question

In a given circle, draw and write the steps of construction -
i. A regular polygon
ii. A regular decagon

Answer 1

1. Regular polygon

Draw a straight line using the protractor. This will be the center line of your circle (dividing it into hemispheres).
Align the protractor with both 0° and 180°on the center line, then 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 the both the 0°and 180° protractor markings on the center line.
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.

• 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 comes out to be 30° and α=30°.

Mark a point for each of the successive angles. Using the protractor, mark all the multiples of the angle α calculated above.
Join the points marked on the circle with a line segment. 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 rub out the circumscribed circle.