Fig. 114.
Ex. 10.—Through two given points to describe an arc of a circle with a given radius, [Fig. 113]. On the points A and B as centers, with the given radius, describe arcs cutting at C; and from C, with the same radius, describe an arc A B as required.
Second, for a circle or an arc, [Fig. 114]. Select three points A, B, C in the circumference, well apart; with the same radius describe arcs from these three points cutting each other, and draw two lines D E, F G, through their intersections according to [Fig. 107]. The point where they cut is the center of the circle or arc.
Ex. 11.—To describe a circle passing through three given points, [Fig. 114]. Let A, B, C be the given points and proceed as in last problem to find the center O, from which the circle may be described.
This problem is variously useful; in finding the diameter of a large fly-wheel, or any other object of large diameter when only a part of the circumference is accessible; in striking out arches when the span and rise are given, etc.
Fig. 115.
Ex. 12.—To draw a tangent to a circle from a given point in the circumference, [Fig. 115]. From A set off equal segments A B, A D, join B D and draw A E, parallel to it, for the tangent.
