 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 11by George Albert Wentworth, David Eugene Smith - 1910 - 287 pagesFull view - About this book
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
| |
