Steps for its construction are as follows:
Step 1: 1st we draw a Circle of specific radius on circle on x - axis of Cartesian system using a compass.
Step 2: We measure the Diameter of circle using compass. Next we place the compass on Intersection points on x – axis simultaneously where the circle intersects with axis and then we draw two arcs from each of the Point. We must get two intersection points for these arcs, one above the circle and another one below the circle. We join the two intersection points.
Step 3: Next we draw an arc from right intersection point of circle of measure equals to the distance between this point and the Center of Circle. This arc is drawn inside the circle forming a Semicircle.
Step 4: Next we join two points of intersection of this arc with the circle. Then we join the point of intersection of the line with x – axis with topmost point of the circle where the line we drew in the beginning intersects. Next draw a small arc of measure equals to the distance between the points of intersection of this line from the center of circle.
Step 5: Next we take the measure of distance between the point of intersection of initial line and the one we got by the arc we drew on joining line and draw another arc that intersects the circle.
Step 6: Finally we take the measure of circle’s right side intersecting point from the arc’s intersecting point that we got in previous step and draw the semicircles within the original circle till we reach the original Position. By joining the vertices of points of intersection of these semicircles, we get our icosagon which looks like: