Elementary plane geometry : inductive and deductive / by Alfred Baker . previous question. 110 Geometry. 16. Is there any position which three points can occupy withrespect to one another, such that a circle cannot be described to passthrough all ? 17. ABCD is a quadrilateral ; A = 85°. B = 80°, C = 95°; AB=60 andBC = 80 millimetres. Construct the quadrilateral and describe acircle about it. 18. AB ( = .3 in.) and CD (=2 in.) are parallel and 1 in. apart. Aline at right angles to one and through its bisection passes alsothrough the bisection of the other. Describe a circle to pass throughA, B,
Elementary plane geometry : inductive and deductive / by Alfred Baker . previous question. 110 Geometry. 16. Is there any position which three points can occupy withrespect to one another, such that a circle cannot be described to passthrough all ? 17. ABCD is a quadrilateral ; A = 85°. B = 80°, C = 95°; AB=60 andBC = 80 millimetres. Construct the quadrilateral and describe acircle about it. 18. AB ( = .3 in.) and CD (=2 in.) are parallel and 1 in. apart. Aline at right angles to one and through its bisection passes alsothrough the bisection of the other. Describe a circle to pass throughA, B, C, D. 19. A line AB is 3 in. long. Describe a circle of radius 3 in. totouch AB at A. Describe a second circle to touch the previous oneand also AB at B. 20. From the fact that two tangents from the same point to a circleare equal, what relation can you establish between the sums of theopposite sides of a quadrilateral whose sides touch a circle ? 21. Construct a quadrilateral whose sides are 40, 30, 50 and 60millimetres, and inscribe a circle in iU CHAPTER Sauares and Circles In and About Circles andSquares. 1. To inscribe a square in a circle, draw twodiameters at right angles to oneanother and join their extrem-ities. The construction beingaccurately made, the set-square-^dll show that the angles A, B,C, D are all right angles; andthe equality of the sides AB,BC, . . may be proved byusing the dividers. Of course the evident equality of the triangles AOB,BOC, . . proves the equality of the sides, and theangles ABC, BCD . . are all right angles, becausethey are angles in semicircles. Inscribe a square in a circle of radius 40 the accuracy of your construction by examining,with the dividers, the equality of the sides. Inscribe a rectangle (which is not also a square) ina circle. Test the accuracy of your construction byexamining, with the set-square, whether the angles areall right angles. In a circle whose radius is 3 inches, inscribe a rect-angle, o
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