 | 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 - 1913 - 486 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 O', AB = A'B'. AB = A'B'. To prove Proof STATEMENTS Draw OA, OB, OA', and... | |
 | 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... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...congruent to A CLM (?). Hence Z o = ZC (?). .'. arc AB = arc LM (193). QED PROPOSITION V. THEOREM 197. In the same circle (or in equal circles) equal arcs are subtended by equal chords. [Converse.] Given : OO = OC ; arc AB = arc LM. To Prove : Chord AB = chord LM. Proof : Draw the several... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...the endpoints of an arc subtends (stretches under or across) the arc. 283. Theorem: In the same or equal circles equal arcs are subtended by equal chords; and conversely, equal chords subtend equal arcs. The truth of the theorem is easily shown by the method of superposition. To prove the converse, draw... | |
 | Mathematics - 1917 - 284 pages
...the circumference. 85b. The arc intercepted by the straight line is said to be subtended by it. 86a. Theorem: In the same circle or in equal circles, equal arcs are subtended by equal chords. Given: In the equal ® the centers of which are 0 and C, let arcs AB and ED be equal. To Prove: Chord... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...intercept equal arcs, and equal arcs are intercepted by equal central angles. [281] 447. In the same or equal circles equal arcs are subtended by equal chords;...and, conversely, equal chords subtend equal arcs. [283] 448. If two tangents to the same circle intersect, the distances from the point of intersection... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 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', AB = A'B'. To prove AB = A'B'. Proof STATEMENTS Draw OA, OB, OA', and... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...Prop. 104. In the same circle, or in equal circles, equal chords subtend equal arcs. Prop. 105. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Prop. 108. The diameter perpendicular to a chord bisects the chord and the arcs subtended by it. Prop.... | |
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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. 
