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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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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...CONVERSELY : In the same circle, or equal circles, if two chords are unequally distant from the centre, they are unequal, and the chord at the less distance is the greater. In the circle whose centre is O, let AB and CD be unequally distant from O; and let OK perpendicular...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 258 pages
...OH, or its equal OF, is greater than OG. PROPOSITION XIII. THEOREM. 167. (Converse of Prop. XII.) In the same circle, or in equal circles, if two chords are unequally distant from the centre, the more remote is the less. In the circle ABD, let chord AB be more remote from the centre...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...distance. 238. In the same circle, or equal circles, if two chords are unequally distant from the centre, they are unequal, and the chord at the less distance is the greater. 239. A straight line perpendicular to a radius at its extremity is a tangent to the circle. 240. Cor....
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...Therefore AB is farther from the centre than CD. QED PROPOSITION XV. THEOREM. 166. CONVERSELY—In the same circle, or in equal circles, if two chords are unequally distant from the centre, the more remote is the less. Given—The chord AB in the circle ABD farther from the centre...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...But, OH>OK. And, OK > OG. (?) PROP. XIII. THEOREM. 167. (Converse of Prop. XII.) In the same cirde, or in equal circles, if two chords are unequally distant from the centre, the more remote is the less. Given 0 the centre of QABC, and chord AB more remote from 0 than...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1898 - 250 pages
...distance from 0 than c' is from 0'. [Gen. Ax. [Why? [? [ 42 (4). [? PROPOSITION XXXII. THEOREM. 163. In equal circles, if two chords are unequally distant from the center, the one at less distance from the center is the greater chord. EXERCISES. 1. Through a given point...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...intersection. EM > EG. (?) EK>EM. (?) Much more is EK > EG. .-. EF>EG. (?) Proposition HO. Theorem. 143. In the same circle, or in equal circles, if two chords are unequally distant from the centre, the chord at the less distance is the greater. Use the indirect method. Ex. 258. The shortest...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...OH= OF. ( 164) But, OH>OK. And, OK> OG. (?) PROP. XIII. THEOREM. 167. (Converse of Prop. XII.) In the same circle, or in equal circles, if two chords are unequally distant from, the centre, the more remote is the less. Given O the centre of OABC, and chord AB more remote from O than...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...< OH. 153 . But OH = OF. 249 .-.OE<OF. O..ED PROPOSITION VIII. THEOREM. 251. CONVERSELY : In the same circle or in equal circles, if two chords are unequally distant from the centre, they are unequal; and the chord at the less distance is the greater. tig_ In the circle whose...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...OF. 249 .-.OE<OF. QED ARCS, CHORDS, AND TANGENTS. PROPOSITION VIII. THEOREM. 251. CONVERSELY : In the same circle or in equal circles, if two chords are unequally distant from the centre, they are unequal; and the chord at the less distance is the greater. In the circle whose centre...
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