With 0 as a center and a radius of 1 3/8 inches draw the given circle. With the T-square draw the diameter A D. With D as a center, and a radius equal to 0 D, describe arcs cutting the circumference at C and E. Now with C and E as centers and the same radius, draw the arcs, cutting the circumference at B and F. Draw the hexagon by joining the points thus formed.

Therefore, in order to inscribe a regular hexagon in a circle, mark off chords equal in length to the radius.

To inscribe an equilateral triangle in a circle the same method may be used, the triangle being formed by joining the opposite vertices of the hexagon.

Proof

Since the triangle 0 C D is an equilateral triangle by construction, the angle C 0 D is one-third of two right, angles and one-sixth of four right angles. Hence arc C D is one-sixth of the circumference and the chord is a side of a regular hexagon.