 | Adelia Roberts Hornbrook - Geometry - 1895 - 224 pages
...each arc by a chord. Superpose and show the truth of the following principle : PRINCIPLE 11. — In the same circle or in equal circles equal arcs are subtended by equal chords. 84. Given the angle ABC 40° ; how many degrees has the angle formed by prolonging CB to D? By prolong-... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 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... | |
 | George Albert Wentworth - Geometry - 1899 - 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... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 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... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...A ABE = A CDE. (?) .-. ZAEB = Z CED. (?) .-. arc AB = arc CD. (?) Proposition 99. Theorem. 132. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Proposition 1OO. Theorem. 133. In the same circle, or in equal circles, if two chords are unequal,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 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', arc AB = arc A'B'. To prove AB = A'B'. Proof. Draw radii, OA, OB, O'A',... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 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... | |
 | 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 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', 76 THE CIRCLE Proof. Draw radii, OA, OB, O'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... | |
| |
THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. 
