Ex. 57. Express in terms of the radius R the area of the segment of a circle whose chord is a side of the inscribed square. Ex. 58. Repeat Ex. 57 if the chord is the side of the equilateral inscribed triangle. Ex. 59. The arch ABC is a lancet crch. It consists of two arcs with equal radii, drawn from centers C1 and C2 out side the span BC. Within the arch are two other lancet arches. Let BC = 2a; let C1C2 = 8; let BD = DC. (a) Determine the height h of the arch BAC. (b) What is the length of the radius of the arc XD? (c) What is the height of the arch BXD? A (d) What is the radius of the circle indicated as tangent to the arches ? (e) What is the area and circumference of the circle? Ex. 60. In a given circle, inscribe three equal circles, tangent to each other and to the given circle. B Ex. 61. In a given equilateral triangle, inscribe three equal circles, tangent to each other and each tangent to one and only one side of the triangle. F B D Ex. 62. The figure below at the left is a quatrefoil. 8 B (a) Construct such a figure based upon a square whose side is 2 in. (b) What is the length of the curved line if ABs inches ? (c) What is the area within the curved line if AB = s inches? (d) Notice that the quatrefoil is used in the adjoining design. Ex. 63. Construct a figure like Fig. 1, below, upon a square of side 2 in. (a) What is the length of the curved line when the side of the square is s inches? (b) What is the total area within the curved line when the side of the square is s inches ? (c) Notice that the curved line of Fig. 1 is the fundamental unit of the adjoining window design. INDEX Altitude, of a □, § 131; of a trap- | Axioms, list of, § 51, § 61, § 90, ezoid, § 145; of a ▲, § 85. Angle, § 20; acute, § 30; central, Angles, adj., § 24; alt.-int., § 92; Arc, 179; minor, § 179; major, § 179; measure of, § 214; inter- § 335. $158. Axis of symmetry, § 427. Base, of a □, § 131; of a ▲, § 68; Bases, of a, § 131; of a trape- Bisect a segment, §78; an angle, Broken line, § 5. Center, of a O, § 16; of gravity, Chord, § 184. Circle, § 16; arc of, § 179; area of, Circles, concentric, § 176; equal, Axiom, § 51; of congruence, § 61; Commensurable, § 211. of limits, § 402; of Ils, § 90. Complement, § 36. Conclusion, § 52. Concurrent lines, § 168. Congruence, § 59; axiom of, § 61. Consequent, § 242. Constant, § 401. Converse, § 104. Corollary, § 71. Degree, of angle, § 28; of arc, § 214. Equal, angles, § 21; ©, § 17; seg- Extreme and mean ratio, § 377. Homologous parts, § 65; sides of Hypothesis, § 52. In-center, § 169, § 226. Incommensurable, § 211; cases, Indirect method, § 94. Locus, § 229. Maximum, § 433. Measure, numerical, § 210; common, Median, of A, §79; of trapezoid, Mid-point of a segment, § 15. Ortho-center, § 171. Parallel lines, § 89; axiom of, § 90; Parallelogram, § 131; altitude of, Perpendicular-bisector, § 76; con- Point, § 4, note p. 27; mid-, § 15; of Points, of intersection, § 10; locus Inscribed, angle, § 216; polygon, Polygon, § 125; 4 of, § 125; diag- |