 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...What is the locus of the mid-points of a system of parallel chords ? [II, § 109 109. Theorem IV. In the same circle or in equal circles, equal chords...that are equally distant from the center are equal. FIG. 80 Given the equal chords AB and A'B' in the equal © O and O'. To prove that AB and A'B' are... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 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...distant from the center ; and, conversely, chords equally distant from the center are equal. I. Given in O ABCD chord AB = chord CD, OE±AB, OH± CD.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...the circle is equally distant from the feet of the perpendiculars. PROPOSITION XIII. THEOREM 208. In the same circle (or in equal circles) equal chords are equally distant from the center. Given : O o ; chord AB = chord CD, and distances OE and OF. To Prove : OE = OF. Proof: Draw radii OA... | |
 | William Betz - Geometry - 1916 - 536 pages
...within the angle, several images of the object will appear. These will lie on a circle. Explain. 264. In the same circle, or in equal circles, equal chords...equally distant from the center; and, conversely, chords equally distant from the center are equal. C Given the circle 0 in which the chords AB and CD are equal.... | |
 | 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...distant from the center ; and, conversely, chords equally distant from the center are equal. 270. A straight line perpendicular to a radius at its extremity... | |
 | 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 0C and... | |
 | 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, O'C'±A'B', OC"±A"B'\... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...perpendicular to a chord. (3) A chord is bisected by a line. (4) A minor arc is bisected. 3. In the same or equal circles equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal. 4. The arcs included between two parallel secants are equal;... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...bisected by a line. 4. A minor arc is bisected. 5. A major arc is bisected. [284] 450. In the same or equal circles equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal. [285] 451. The arcs included between two parallel secants... | |
 | 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...distant from the center ; and, conversely, chords equally distant from the center are equal. I. Given in O ABCD chord AB = chord CD, OE -L AB, OH A.... | |
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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. 
