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" The perpendicular bisector of a chord passes through the center of the circle and bisects the arcs subtended by the chord. "
New Plane and Solid Geometry - Page 121
by Wooster Woodruff Beman, David Eugene Smith - 1899 - 382 pages
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...to it. For v AE = EC, and OA = OC, and OE = OE, .'. A AEOSS A CEO, and Z OEA = Z CEO, by I, th. 12. 2. The perpendicular bisector of a chord passes through...on the perpendicular bisector of the chord, by I, th. 29. Theorem 6. All points in a chord lie within the circle; and all points in the same line, but...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...perpendicular to it. ForvAE=EC, and OA = OC, and OE = OE, .-. A AEO-S A CEO, and Z OEA = Z CEO, by I, th. 12. 2. The perpendicular bisector of a chord passes through...center of the circle and bisects the subtended arcs. Theorem 6. All points in a chord lie within the circle; and all points in the same line, but not in...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...OC, .'. DB has two points equidistant from A and C. Hence, being determined by these points, it is J_ to AC, by I, prop. XLI. 2. The perpendicular bisector...center of the circle and bisects the subtended arcs. PROPOSITION VI. 185. Theorem. All points in a chord lie within the circle ; and all points in the same...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...is the usual means of proving : (1) The equality of lines ? (2) The equality of arcs ? 179. COR. A perpendicular bisector of a chord passes through the center of the circle. Ex. 313. If two chords are equal, the perpendiculars from the center upon the chords are equal. Ex....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...What is the usual means of proving: (1) The equality of lines ? (2) The equality of arcs ? 179. COR. A perpendicular bisector of a chord passes through the center of the circle. Ex. 313. If two chords are equal, the perpendiculars from the center upon the chords are equal. Ex....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...is the usual means of proving : (1) The equality of lines ? (2) The equality of arcs ? 179. COR. A perpendicular bisector of a chord passes 'through the center of the circle. Ex. 313. If two chords are equal, the perpendiculars from the center upon the chords are equal. Ex....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...is the usual means of proving : (1) The equality of lines ? (2) The equality of arcs ? 179. COR. A perpendicular bisector of a chord passes through the center of the circle. Ex. 313. If two chords are equal, the perpendiculars from the center upon the chords are equal. Ex....
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...to the chord; a diameter which bisects an arc is the perpendicular bisector of that arc. 223. COR. 2. The perpendicular bisector of a chord passes through the center of the circle, and bisects the arcs subtended by the chord. 224. COR. 3. A line from the center perpendicular to a chord bisects the...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...A diameter which bisects a chord (shorter than a diameter) is perpendicular to the chord. 223. COR. 2. The perpendicular bisector of a chord passes through the center of the circle, and bisects the arcs subtended by the chord. 224. COR. 3. A line from the center perpendicular to a chord bisects the...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...bisects a chord (shorter than a diameter) is perpendicular to the chord. 223. COR. 2. The prrpendicular bisector of a chord passes through the center of the circle, and bisects the arcs subtended by the chord. 224. COR. 3. A line from the center perpendicular to a chord bisects the...
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