Second. To inscribe the square. Draw the two diameters A B, C D at right angles and join the points A B, C D to form the square.
In the same way a circle may be described about a triangle.
Fig. 125.
Ex. 20.—To inscribe a circle on a square, and to describe a square about a circle, [Fig. 125].
First. To inscribe the circle. Draw the diagonals A B, C D of the square, cutting at E; draw the perpendicular E F to one side, and with the radius E F describe the circle.
Second. To describe the square. Draw two diameters A B, C D at right angles, and produce them; bisect the angle D E B at the center by the diameter F G, and through F and G draw perpendiculars A C, B D, and join the points A D and B C where they cut the diagonals to complete the square.
Fig. 126.
Ex. 21.—To inscribe a circle in a triangle, [Fig. 126]. Bisect two of the angles A C of the triangle by lines cutting at D; from D draw a perpendicular D E to any side, and with D E as radius describe a circle.