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given line, and as the angle in a semi-circle is always a right angle, the problem is to draw a semi-circle that shall contain the three angular points of a right-angled triangle, one of which is the given point in the problem. Problem 4 (Fig. 47). To bisect (or divide into two equal parts) a given angle. When speaking of an angle, it is usual to name it by affixing either a single letter at the angular point, or a letter to each of its lines and the angular point, the one denoting the latter being always the second, In the problem, let BAG be the given angle. With any convenient radius set off from A equal distances on BA and CA in the points D and E, and from these points, with a radius greater than half the distance across from D to E, draw arcs intersecting in F ; a line through F and A will bisect the angle BAG. This construction, it MECHANICAL AND ENGINEERING DF AWING 25 Fig. O . Fig. 4o Fig: 44 Fig. 4$ Fig. 4$ Fig. 47 c Fig. 48 Fig. 49 Fig. 50