 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
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...L. 4. .'. OL<OK. . Why? 5. But OF<OL. Why? .-.OF<OK, Why? or OF<OH. PROPOSITION VI. THEOREM 267. In the same circle, or in equal circles, if two chords...the 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... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...L. 4. .'. OL<OK. Why? 5. But OF<OL. Why? ... OF<OK, Why? or OF< OH. PROPOSITION VI. THEOREM 267. In the same circle, or in equal circles, if two chords...the 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... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...bisects the chord.) BntAB>CD. Given .-. AB >AE, the equal of CD. Ax. 9 .'. AP>AR. Ax. 6 .-.ZARP>Z-RPA. §113 (If two sides of a A are unequal, the A opposite...center 0, two chords AB and CD unequally distant from O, and OP, the perpendicular to AB, less than OQ, the perpendicular to CD. To prove that AB > CD. Proof.... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...complement o£-Z.ARP, is less than Z.OPR, the complement of Z RPA. § 59 .\OP<OR.. §114 But OR=OQ. §178 PROPOSITION VIII. THEOREM 180. In the same circle...Proof. Suppose AE drawn equal to CD, and OR _L to AE. 'Now OP<OQ, Given and OR = OQ. § 178 ,'.OP<OR. Ax. 9 Drawing PR, Z.PRO<Z. OPR. § 113 .'. Z ARP,... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...Z.OPR, the complement of Z RPA. § 59 .-.OP<OR. §114 But OR = OQ. § 178 .'. OP<OQ, by Ax. 9. QBD PROPOSITION VIII. THEOREM 180. In the same circle...center 0, two chords AB and CD unequally distant from O, and OP, the perpendicular to AB, less than OQ, the perpendicular to CD. To prove that AB > CD. Proof.... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...< OF. FIG. 81 § 108 Given §78 Ax. 8 § 75 § 109 Ax. 9 111. Corollary 1. (Converse of § 110.) In the same circle or in equal circles, if two chords are unequally distant from the center, the more remote is the less. EXERCISES 1. Show that a board sawed from a circular log is wider than... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...-unequal chords are drawn, the longer one is nearer the center. 111. Corollary 1. (Converse of § 110.) In the same circle (or in equal circles), if two chords are unequally distant from the center, the more remote is the less. PART II. TANGENTS AND SECANTS 115. Theorem VI. A line perpendicular to... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...log, or from equal logs, at equal distances from the center, are equal in width. 95 110. Theorem V. In the same circle, or in equal circles, if two chords are unequally distant from the center, the more remote is the less. Given the OO with- the two chords AB and CD such that AB > CD. Also, let... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...diameter of a smaller concentric circle. Prove AXBY is a parallelogram. 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 OO : OELAB; OF ±CD; OE > OF. Conclusion. AB < CD. Proof.... | |
 | William Betz - Geometry - 1916 - 536 pages
...intersect AB in some point, as £. 4. .\OL<OK. Why? 5. But OF<OL. Why? .-.OF<OK, Why? or OF< OH. 267. In the same circle, or in equal circles, if two chords...the chord at the less distance is the greater. Given the chords AB and CD in a circle 0 ; also OF, the perpendicular to AB, less than OH, the perpendicular... | |
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