When the four tangents make right angles with each other, the figure is a square. In other cases, any di- rection may be given to two of the tangents.
In figure 10 we say the circle is circumscribed by the square, or the circle inscribed in a square*
17. Inscribe a square in a circle. (fig. 11.)
When a polygon has all the points of its angles touch- ing a circle, it is said to be inscribed in a circle, and the circle circumscribes the polygon.
18. Double an arc of a circle. (fig. 6.)
This is more difficult than Prop. 11. First draw an arc and mark the centre of its circle, then prolong the arc to two, three, Stc. times its former size.
19. Draw a tangent to a circle from a given point outside. (fig. 8.)
20. Draw two tangents to a circle from a given point. (fig. 12.)
Observe that in drawing a tangent to a circle in problem 14, any part of the circle may be taken, but when a tangent is drawn from a given point, it can hit but two points of the circle, as in fig. 12.
21. Cut a circle into six equal parts, or, in other words, inscribe a regular hexagon in a circle.) (fig. 13.)
The radius of any circle is equal to one side of the hexagon to be inscribed in it. The monitor, therefore,
(12)
(13)
