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" In the same circle or in equal circles, if two chords are unequally distant from the center, they are unequal, and the chord at the less distance is the greater. "
Wentworth's Plane Geometry - Page 11
by George Albert Wentworth, David Eugene Smith - 1910 - 287 pages
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...arc XY. Suggestion, — Draw radius OF. PLANE GEOMETRY — BOOK II PROPOSITION XII. THEOREM 196. In the same circle or in equal circles, if two chords are unequally distant from the center, the more remote is the smaller. Hypothesis. In O 0 : OE±AB; OF±CD; OE > OF. Conclusion. AB < CD....
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...unequally distant from the center; the greater chord is the less distant. Theorem XV. In the same or equal circles if two chords are unequally distant from the center, they are unequal; the chord less distant is the greater. Corollary. The diameter is the longest chord in a circle. Summary...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...unequally distant from the center; the greater chord is the less distant. Theorem XV. In the same or equal circles if two chords are unequally distant from the center, they are unequal; the chord less distant is the greater. Corollary. The diameter is the longest chord in a circle. Summary...
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Plane Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...L. The line //i is drawn. Prove that the angle LUG is greater than the angle GLH. Theorem 11 186. In the same circle or in equal circles, if two chords are unequally distant from the center, the chord at the greater distance is the less. Given (using the figure of § 185) chords FG'and AB,...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1925 - 504 pages
...chords are = dist. from center. 7. (131). 8. (Ax. 11). 9. (Ax. 9). PROPOSITION VIII. THEOREM 201. In the same circle, or in equal circles, if two chords are unequally distant from the center, the chord at the less distance is the greater. [Converse to Prop. VII.] Given in O ABCD with OE < OF,...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 pages
...point, as L. 4. .'. OL<OK. Why? 5. But OF<OL.. Why? .'. OF<OK, Why? PROPOSITION VI. THEOREM 267. In the same circle, or in equal circles, if two chords...chord at the, less distance is the greater. Given the chords AB and CD in a circle O ; also OF, the perpendicular to AB, less than OH, the perpendicular...
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