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" In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal. "
Plane and Solid Geometry - Page 90
by William James Milne - 1899 - 384 pages
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...triangles, ACE, and ECB, are equal in all respects, and AE = EB. Hence the theorem. THEOREM III. In the same circle, or in equal circles, equal chords are equally distant from the center. Let AB and EF be equal chords, and C the center of the circle. From C, draw CG and CH, perpendicular...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...angles on the same side together equal to two right angles, the two lines are parallel. 3. Prove that in the same circle or in equal circles, equal chords are equally distant from the center; and of two unequal chords, the less is the more remote from the center. 4. Prove that if a line is...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— THEOREM. 18. In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 1st. Let AB,...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— THEOREM. 18. In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 1st. Let AB,...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...than two straight lines drawn to the circumference are equal, that point is the centre, THEOR. n. In the same circle, or in equal circles, equal chords are equally distant from the centre; and of two, unequal chords the greater is nearer to the centre than the less. [First part by...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...lines bisecting the three sides of a triangle at right angles meet in the same point. PROPOSITION VIII. THEOREM.. In the same circle or in equal circles, equal chords are equally distant from the centre; and of two unequal chords, the less is the more remote from the centre. Let the chords AB,...
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...the centre of the circled. * Euclid, in. 10. t Euclid, III. 9. 130 ELEMENTARY GEOMETRY. THEOREM n. In the same circle, or in equal circles, equal chords are equally distant from the centre; and of two unequal chords the greater is nearer to the centre than the less*. First. Part....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 456 pages
...the three sides of a triangle at right angles meet in the same point. PROPOSITION vui. TIIROREM. In the same circle or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is the more remote from the centre. Let the chords AB,...
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The Cambridge Examiner, Volume 1

Education, Higher - 1881 - 504 pages
...rectangle contained by their sum and difference. 5. Senior Paper, No. 2. 6. Senior Paper, No. 4. 7. In the same circle, or in equal circles equal chords are equally distant from the centre ; and of two unequal chords the greater is nearer to the centre than the less. 8. The angle...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...OB, OD = OD; ВA vtOD = RA BOD, AD = BD. ¿- a = ¿- b; &rcAC= arc BC. (186) QED THEOREM VII. 192. In the same circle, or in equal circles, equal chords are equally distant from the centre; and if two chords are unequal, the less is at the greater distance from the centre. Let chord...
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