Inscribe a regular polygon of any number of sides (say n = 5), in a circle

Figure 4 shows the method of inscribing a regular polygon of any number of sides.

• Draw the circle with diameter AB.
• Divide AB in to “n” equal parts
• Number them.
• With center A & B and radius AB, draw arcs to intersect at P.
• Draw line P2 and produce it to meet the circle at C.
• AC is the length of the side of the polygon.

Figure 4 Inscribing a regular polygon of any number of sides.

To draw a circle to touch a given line, and a given circle at a given point on it.

The method is illustrated in figure 5.

• Given: Line AB, circle with centre C and point P on the circle.
• From P, draw a tangent to the circle intersecting AB at D.
• Draw bisector of  angle PDB to intersect the line through C and P at O.
• With center O and radius OP, draw the required circle.

 

Figure 5.  shows the method of drawing a circle to touch a given line and a given circle at a particular point.