Plane and solid geometry . ual parts indicated below: 2, 4, 8, 16,... 2^ 3, 6, 12, 24,... 3x 25, 10, 20, 40, ... 5x 2^^ 15, 30, 60, 120, ... 15 x2J being any positiveinteger]. Construct an angle of 24°. Circumscribe a regular pentedecagon about a given circle. On a given line as one side, construct a regular pente- Ex. 989. Ex. 990. decagon. Ex. 991. Assuming that it is possible to inscribe in a circle aregular polygon of 17 sides, show how it is possible to inscribe a regularpolygon of 51 sides. Ex. 992. If a regular polygon is inscribed in a circle, the tangentsdrawn at the mid-point
Plane and solid geometry . ual parts indicated below: 2, 4, 8, 16,... 2^ 3, 6, 12, 24,... 3x 25, 10, 20, 40, ... 5x 2^^ 15, 30, 60, 120, ... 15 x2J being any positiveinteger]. Construct an angle of 24°. Circumscribe a regular pentedecagon about a given circle. On a given line as one side, construct a regular pente- Ex. 989. Ex. 990. decagon. Ex. 991. Assuming that it is possible to inscribe in a circle aregular polygon of 17 sides, show how it is possible to inscribe a regularpolygon of 51 sides. Ex. 992. If a regular polygon is inscribed in a circle, the tangentsdrawn at the mid-points of the arcs subtended by the sides of the in-scribed polygon form a circumscribed regular polygon whose sides areparallel to the sides of the inscribed polygon, and whose vertices lie onthe prolongations of the radii drawn to the vertices of the inscribedpolygon. 254 PLANE GEOMETRY Propositiox YI. Theorem 530. A circle may he circmnscrihed about any regularpolygon; and a circle may also he inscribed in it. B ^^^ ^^n^. Given regular polygon ABCD - • •. To prove: (a) that a circle may be circumscribed about it;(b) that a circle may be inscribed in it. (a) Argument 1. Pass a circumference through points A, B, and C. 2. Connect 0, the center of the circle, with all the vertices of the OB = OC. .. Z1 = Z ABC = Z BCD. .-. Z3 = Z4. Also AB = A ABO=A OCD. .-. OA = OD and circumference ABCpasses through In like manner it may be proved thatcircumference ABC passes througheach of the vertices of the regularpolygon; the circle will then becircumscribed about the polygon. Reasons 1. § 324. 2. §54,15. 3. § 279, a. 4. § 111. 5. § 515. 6. § 54, 3. <. § 515. 8. § 107. 9. § 110. 0. By steps similar to 1-9. BOOK V 255 (p\ Argument 1. Again AB, BC, CD, etc., the sides of the given polygon, are chords ofthe circumscribed circle. 2. Hence Js from the center of the circle to these chords are equal. 3. /. with 0 as center, and
Size: 1759px × 1421px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
