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New plane and solid geometry (1899)
Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, Ginn & company · leaf 140
notbetween those two points, and hence must lie either within or withoutthe circle. Exercises. 262. Prove that, in general, two chords of a circle can-not bisect each other. What is the exception ? 263. What is the locus of the mid-points of a pencil of parallelchords of a circle ? Why ? Prop. VII.… … Given two equal © M. M, with chords AB = AB, AE >AB, and OC, 01), OC _Ls from center 0 to AB,AE. and from center O1 to AB. To prove that (1) OC=0C, (2) OD < OC Proof. 1. C, C bisect AB, AB, Prop. V AC = AC, being halves of equal chords. Ax. 7OA = OA Draw OA, OA; then and ZC = Z C, Prel. prop.…Geometry
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