37. Inscribe and circumscribe a circle with regular and parallel hexagons. (fig. 23.)
38. Inscribe a circle in a regular hexagon. (fig. 22.) This problem is the inverse of the 36th. First draw
the hexagon, then describe the circle, touching it on all sides. The centre of the circle may be found by rais- ing perpendiculars on the middle of any two sides until they cross each other. The point where they cross, is the centre.
39. Make a triangle whose three sides are given•
Trace three right lines for sides. Take one of them, the longest if you please, for the base, and then make a point where you think the other two sides will reach. The difficulty is to ascertain exactly where this point should be. With dividers it may be easily found in the following manner :—After you have drawn the base, open the dividers the length of the next side to be drawn, and placing one foot of the dividers on one end of the base, draw an arc with the other foot. Then taking the length of the third side, place one foot on the other end of the base, and draw an arc which shall cross the former arc : the point where the arcs cross each other is the summit or apex required.
If the two arcs cannot cross, the problem is said to be absurd : for no triangle can be made of the given sides. Each of the three sides must be shorter than the two others would be if united.
(fig. 24.)
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