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" In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the center, and the greater chord is at the less distance. "
Plane and Solid Geometry - Page 114
by Fletcher Durell - 1911 - 546 pages
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...circles, equal chords are equally distant from the centre ; and conversely. 237. In the same circle, or equal circles, if two chords a.re unequal, they are unequally distant from the centre, and the greater is at the less distance. 238. In the same circle, or equal circles, if two...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...§ 245 § 151 Ax. 7 § 217 § 128 § 151 § 217 Hyp. §128 Ax. 6 PROPOSITION VII. THEOREM. 250. In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the centre; and the greater chord is at the less distance. In the circle whose centre is O, let the chords...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...§ 217 and OP = OH. Hyp. Hence, AP = CH. § 128 .-. AB = CF. Ax. 6 PROPOSITION VII. THEOREM. 250. In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the centre; and the greater chord is at the less distance. In the circle whose centre is 0, let the chords...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...be equal to a given chord and parallel to a given straight line. Proposition 1O9. Theorem. 142. In the same circle, or in equal circles, if two chords are unequal, the less chord is at the greater distance from the centre. Hypothesis. In the O ABC, chord AB < chord...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...OF. (Why?) CONVERSELY. Given circle 0, and AB and CD equidistant from the center. To prove AB= CD. PROPOSITION IX. THEOREM 227. In the same circle, or...from the center than chord AB. Proof. Let OG be drawn J. CD, and OF J. AB. Then chord AB > chord CD. Hyp. .-. arc AB > arc CD, Art. 220. (in the same O,...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...(Why?) CONVERSELY. Given circle 0, and AB and CZ> equidistant from the center. To prove AB=CD. POOR II. PLANE GEOMETRY PROPOSITION IX. THEOREM 227. In...chord is at the greater distance from the center. \J Given in the circle 0 the chord CD < chord AB. To prove that chord CD is at a greater distance from...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...Hence, AP = CH. § 128 .-.AB=CF. Ax. 6 84 BOOK II. PLANE GEOMETRY. PROPOSITION VII. THEOREM. 250. In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the centre ; and the greater chord is at the less distance. In the circle whose centre is O, let the chords...
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Bulletin

Education - 1904 - 738 pages
...angles of a polygon, made by producing each of its sides in succession, is equal to ... 3 Prove that in the same circle or in, equal circles if two chords are unequal, the greater chord is at the less distance from the center. 4 Prove that two triangles are similar if...
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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...

Cora Lenore Williams - Geometry - 1905 - 56 pages
...equal circles, the greater of two unequal minor arcs is subtended by the greater chord. Prop. 52. In the same circle, or in equal circles, if two chords are unequal, the greater subtends the greater minor and the less major arc. Prop. 53. In the same circle, or in...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...(?). .-. AE= CF (?). AB is twice AE and CD is twice OF (?). .-. .4B = CD (Ax. 3). QED 223. THEOREM. In the same circle (or in equal circles) if two chords are unequal, the greater chord is at the less distance from the center. Given : O o ; chord AB > chord CD, and distances...
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