 | Arthur Schultze - 1901 - 260 pages
...then said to be circumscribed about the polygon. PROPOSITION II. THEOREM 177. In the same circle, or equal circles, equal arcs are subtended by equal chords;...and, conversely, equal chords subtend equal arcs. Hyp. In equal ©, O and O', Proof. Draw radii, OA, OB, O'A', O'B'. Z AOB = Z A'O'B', {equal arcs subtend... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...with O'D', and the angle COD will coincide with the angle C'O'D'. Therefore, etc. PROPOSITION VI. — THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal clwrds; and, CONVERSELY, equal chords subtend equal arcs. Given. — In the two equal circles whose... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...equal central angles; and of two unequal arcs the greater subtends the greater central angle. 241. In the same circle or in equal circles, equal arcs are subtended by equal chords; and of two unequal arcs the greater is subtended by the greater chord. 249. In the same circle or in equal... | |
 | Education - 1902 - 880 pages
...figure is a parallelogram. 3 Prove that two mutually equiangular triangles are similar. 4 Prove that in the same circle or in equal circles equal arcs are subtended by equal chords. State th*e converse of this theorem. 5 Complete and demonstrate the following: the area of a regular... | |
 | Education - 1902 - 780 pages
...figure is a parallelogram. 3 Prove that two mutually equiangular triangles are similar. 4 Prove that in the same circle or in equal circles equal arcs are subtended by equal chords. State the converse of this theorem. 5 Complete a.nd demonstrate the following: the area of a, regular... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...no proof like that given in the text is required to establish it. PROPOSITION III. THEOREM. 241. In the same circle or in equal circles, equal arcs are subtended by equal chords; and of two unequal arcs the greater is subtended by the greater chord. In the equal circles whose centres... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...part of it that is both a segment and a sector. BOOK II. PLANE GEOMETRY PEOPOSITIOK V. THEOREM 219. In the same circle, or in equal circles, equal arcs are subtended by equal chords. B" Given the equal circles 0 and 0', and arc AB = arc A'B'. To prove chord AB = chord A'B'. Proof.... | |
 | Isaac Newton Failor - Geometry - 1904 - 100 pages
...triangle. 328. Circumscribe a circle about an equilateral triangle. 329. Show by superposition that in the same circle or in equal circles equal arcs are subtended by equal chords. 330. Mark a point P within a circle and draw through it the longest and the shortest possible chords... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...part of it that is both a segment and a sector. BOOK II. PLANE GEOMETEY PROPOSITION V. THEOREM 219. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Given the equal circles 0 and 0', and arcJ_jB = arc ArBf. To prove chord AB = chord A'Bf . Proof «... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...the center. 218. In the same circle, or in equal circles, equal chords | subtend equal arcs. 219. In the same circle, or in equal circles, equal arcs are subtended by equal chords. 220. In the same circle, or in equal circles, the greater of two (minor) arcs is subtended by the greater... | |
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In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. 
