 Theorem. In the same circle, or in equal circles, equal chords are equally distant from the center; conversely, chords equally distant from the center are equal.  Plane Geometry - Page 90by William James Milne - 1899 - 242 pagesFull view - About this book
 | Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...(a) Chord BE = chord BD. (b) Arc AE = arc AD. (c) Chord AE= chord AD. PROPOSITION IV. THEOREM 212. In the same circle or in equal circles, equal chords are equally distant from the center, and conversely. Given the equal circles 0 and 0', with chord AB = chord EF. To prove that the perpendiculars... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...circle. 252. A diameter perpendicular to a chord bisects the chord and the arcs subtended by it. 264. In the same circle or in equal circles equal chords are equally distant from the center ; and, conversely, chords equally distant from the center are equal. 270. A straight line perpendicular... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...To a given circle draw a tangent that shall be parallel to a given line. 285. Theorem: In the same, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal. Given OO = OO', AB=A'B' = A"B" OC±AB,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...To find the center of a given circle. Ex. 616. To bisect a given arc. PROPOSITION V. THEOREM 197- In the same circle, or in equal circles, equal chords are equally distant from the center ; and, conversely, chords equally distant from the center are equal. I. Given in O ABCD chord AB =... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...280. Theorem. The perpendicular bisector of a chord passes through the center of the circle. § 281. Theorem. In the same circle or in equal circles, e,qual chords are equidistant from the center. Conversely: Chords equidistant from the center are equal. § 282. The... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...within a given circle. Through this point draw a chord which shall be bisected at that point. 281. Theorem. In the same circle or in equal circles, equal chords are equidistant from the center. Conversely: Chords equidistant from the center are equal. Given chord... | |
 | Education - 1921 - 1190 pages
...tangent to a circle at a given point is perpendicular to the radius at that point; and conversely. 26. In the same circle or in equal circles, equal chords are equally distant from the center; and conversely. 27. An angle inscribed in a circle is equal to half the central angle having the same... | |
 | National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...tangent to a circle at a given point is perpendicular to the radius at that point; and conversely. 26. In the same circle or in equal circles, equal chords are equally distant from the center; and conversely. 27. An angle inscribed in a circle is equal to half the central angle having the same... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...To find the center of a given circle. Ex. 516. To bisect a given arc. PROPOSITION V. THEOREM 197. In the same circle, or in equal circles, equal chords are equally distant from the center ; and, conversely, chords equally distant from the center are equal. I. Given in O ABCD chord AB =... | |
 | Edson Homer Taylor, Fiske Allen - Mathematics - 1923 - 104 pages
...of contact, and the arcs subtended by the chord. Prove this theorem. THEOREM XXIII 143. In the same or in equal circles equal chords are equally distant from the center. 144. Analysis. To prove two chords equally distant from the center, what lines must be proved equal?... | |
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