96. Any angle can be trisected fairly accurately by paper folding, and in this way we may construct approximately the regular nonagon.

Fig. 35.

Obtain the three equal angles at the center of an equilateral triangle. (§ 25.)

For convenience of folding, cut out the three angles, AOF, FOC, and COA.

Trisect each of the angles as in Fig. 35, and make each of the arms = OA.

97. Each of the angles of a nonagon is 14/9 of a right angle = 140°.

The angle subtended by each side at the center is 4/9 of a right angle or 40°.

Half this angle is 1/7 of the angle of the nonagon.

98. OA =½a, where a is the side of the square; it is also the radius of the circumscribed circle, F.

The radius of the inscribed circle =R . cos20° = ½a cos 20°

= a/2 X 0.9396926

= a X 0.4698463. The area of the nonagon is 9 times the area of the triangle AOL

= 9.R.½ R sin40°

= 9/2 R2. sin 40°

= 9a2 / 8 X 0.6427876 = a2 X 0.723136.