 Theorem. In the same circle or in equal circles, equal chords are equidistant from the center; and of two unequal chords the greater is nearer the center. Given two equal © M, M ' , with chords AB = A'B', AE > A'B', and OC, OD, O'C' ±'s from center...  Plane Geometry - Page 94by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1915 - 277 pagesFull view - About this book
 | Elias Loomis - Conic sections - 1877 - 458 pages
...lines bisecting the three sides of a triangle at right angles meet in the same point. PROPOSITION VIII. THEOREM.. In the same circle or in equal circles, equal chords are equally distant from the centre; and of two unequal chords, the less is the more remote from the centre.... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...arc, and is perpendicular to the chord. [Let the student give the demonstration.] PROPOSITION VI. 150. Theorem. — In the same circle, or in equal circles, equal chords are equally distant from the centre. DEMONSTRATION. Let EF and GH be equal chords in the same circle or... | |
 | George Albert Wentworth - Arithmetic - 1886 - 392 pages
...then have the same extremities, and the chords AB and CD will coincide and be equal. AM FIG. 18. 367. THEOREM. In the same circle, or in equal circles, equal chords are equally distant from the centre. Let AB and CD be two equal chords in the two equal circles whose centres... | |
 | George Albert Wentworth - 1889 - 276 pages
...only one. 84. Corollary. If two circumferences have three points common, they coincide throughout. 85. Theorem. In the same circle, or in equal circles, equal chords are equally distant from the centre; and conversely. 86. Theorem. In the same circle, or in equal circles,... | |
 | George Albert Wentworth - 1889 - 264 pages
...one. • 84. Corollary. If two circumferences have three points common, they coincide throughout. 85. Theorem. In the same circle, or in equal circles, equal chords are equally distant from the centre; and conversely. 86. Theorem. In the same circle, or in equal circles,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...not between those two points, and hence must lie either within or -without the circle. Theorem 7. In the same circle or in equal circles, equal chords are equidistant from the center; and of two unequal chords the greater is nearer the center. Given two equal © M, M', with chords AB... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...not between those two points, and hence must lie either within or without the circle. Theorem 7. In the same circle or in equal circles, equal chords are equidistant from the center; and of two unequal chords the greater is nearer the center. Given two equal © M, M', with chords AB... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...general, two chords of a circle cannot bisect each other. What is the exception ? PROPOSITION VII. 186. Theorem. In the same circle or in equal circles, equal chords are equidistant from the center; and of two unequal chords the greater is nearer the center. Given two equal © M, M ' , with chords... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...the locus of the mid-points of a pencil of parallel chords of a circle ? Why ? PROPOSITION VII. 186. Theorem. In the same circle or in equal circles, equal chords are equidistant from the center; and of two unequal chords the greater is nearer the center. Given two equal © M, M', with chords AB... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...Draw a circle and two chords equally distant from the center. How do the chords compare in length ? 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. Data:... | |
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