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of the sides, and then on the middle of another side. These perpendiculars will cross each other, and the point of section (that is, the point where they cut each other) will be the centre of the circle required.
In the figure, the dotted lines show the perpendiculars and centre.
29. Make a circle, and draw a tangent triangle. (fig. 19.)
Three tangents to a circle are easily made, but the monitor may increase the difficulty by giving directions to the tangent sides. Thus, let two sides be at right angles, obtuse or acute; let the triangle be equilateral, &c.
30. Draw a regular pentagon, and circumscribe it with a circle. (fig. 17.)
31. Draw a regular hexagon, and circumscribe it with a circle. (fig. 13.)
32. Draw a regular octagon, and circumscribe it with a circle. (fig. 16.)
In the former problems, the circle was made first, now the polygon.
33. Inscribe a circle in a triangle. (fig. 19.)
To find the centre of the circle, draw a line from the middle of either side of the triangle to the apex opposite, then do the same by another side and its opposite apex; the place where these two lines cross each other, will be the centre of the circle to be inscribed. See the dotted lines in fig. 19.
34. Make an arc which shall pass through two given points. (fig. 20.)
