 In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.  Elements of Geometry - Page 24by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
 | Cora Lenore Williams - Geometry - 1905 - 50 pages
...Def. 45. The straight line joining any two points on a circumference is called a chord. Prop. 18. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Prop. 19. In the same circle, or in equal circles, equal chords subtend equal arcs. to the middle point... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...Chord AB = chord LM (Hyp.). .-.A OAB = A CLM (?). .-. arc AB = arc LM (?) (206). QED 210. THEOREM. In the same circle (or in equal circles) equal arcs are subtended by equal chords. Given : OO = OC ; arc AB = arc LM. To Prove: Chord AB = chord LM. Proof : Draw the several radii to... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...Chord AB = chord LM (Hyp.). .-.A OAB = A CLM (?). .-. arc AB = arc LM (?) (206). QED 210. THEOREM. In the same circle (or in equal circles) equal arcs are subtended by equal chords. Given : OO = OC ; arc AB = arc LM. To Prove: Chord AB = chord LM. Proof : Draw the several radii to... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...angles intercept unequal arcs on the circumference, and conversely. PROPOSITION XXVI 95. Theorem: In the same circle or in equal circles, equal arcs are subtended by equal chords, and conversely. I. Given circle O, with arc AB=arc CD (Fig. 63). FIG. 63 To prove chord AB =chord C D. This is left... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...or in equal circles, sectors with equal central angles are equal. PROPOSITION II. THEOBEM. 233. In the same circle, or in equal circles, equal arcs are subtended ~by equal chords and intercepted by equal central angles. Given OC = O C' and arc AB = arc A'B'. To prove chord AB= chord... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...circumference. The circle is then said to be circumscribed about the polygon. PROPOSITION II. THEOKEM 177. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. Hyp. In equal ©, 0 and 0', Proof. Draw radii, OA, OB, O'A', O'B'. Z AOB = Z A'O'B', (equal arcs subtend... | |
 | Education - 1904 - 484 pages
...This and similar exercises may be assigned as home work. EXERCISE 79. Show by superposition that in the same circle, or in equal circles, equal arcs are subtended by equal chords; that equal chords are equidistant from the centre. After following the directions of the above in several... | |
 | Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...to be inscribed in the segment ABC. The angle A is inscribed in segment CAB. THEOREM LVIII 244. In the same circle or in equal circles, equal arcs are subtended by equal chords. Use figure in § 238. Draw chords BA and B'A'. Prove A OAB = A O'A'B'. 245. The converse of this theorem... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...the included angle of the other. 213. Radii of the same circle or of equal circles are equal. 233. In the same circle, or in equal circles, equal arcs are subtended by equal chords and intercepted by equal central angles. 234. In the same circle, or in equal circles, equal chords subtend... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...the circumscribed circle is called the circumcenter of the polygon. PROPOSITION II. THEOREM 188. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. I. Given in equal ©, 0 and 0', To prove AB = A'B'. Proof STATEMENTS Draw OA, OB, OA', and OB'. Z AOB... | |
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