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" The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference. Angles in the same segment of a circle are equal ; and, if the line joining two points... "
Calendar - Page 120
by University of Calcutta - 1907
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Two Geometrical Memoirs on the General Properties of Cones of the Second ...

Michel Chasles - Cone - 1837 - 564 pages
...we may be permitted to add the following, which are derived from known properties of the circle. (1) The angle which an arc of a circle subtends at the centre is double ofthat which it subtends at any point in the remaining part of the circumference. Hence, If from two...
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Two geometrical memoirs of the general properties of cones of the second ...

Michel Chasles - 1841 - 130 pages
...we may be permitted to add the following, which are derived from known properties of the circle. (1) The angle which an arc of a circle subtends at the centre is double of that which it subtends at any point in the remaining part of the circumference. Hence, If from two...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 486 pages
...intercepted on it by two given circles are equal to two given straight lines. 15—2 220 PROPOSITION 20. The angle which an arc of a circle subtends at the centre is double of the angle which the arc subtends at the circumference. Let ABC be a circle, of which BC is an arc,...
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Examinations Papers

1894 - 786 pages
...and least lines which can be drawn from that point to the circumference. 8. The angle which a chord of a circle subtends at the centre is double that which it subtends at any point on that part of the circumference which lies on the same side of it as the centre. 9. Show how to describe...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...intercepted on it by two given circles are equal to two given straight lines. 15—2 220 PROPOSITION 20. The angle which an arc of a circle subtends at the centre is double of the angle which the arc subtends at the circumference. Let ABC be a circle, of which BC is an arc,...
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The School World: A Monthly Magazine of Educational Work and Progress, Volume 5

Education - 1903 - 692 pages
...tangent at any point of a circle and the radius through the point are perpendicular to one another. If two circles touch, the point of contact lies on...circle subtends at the centre is double that which it tends at any point on the remaining part of the circumference. Angles at the same segment of a circle...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...ABC is produced, through the vertex A, to a point D. Prove that ^.DAC = 24.ABC.— 2^.ACB. THEOREM 8. The angle which an arc of a circle subtends at the...point on the remaining part of the circumference. fig. 241. fig. 242. Data The arc ACB of 0ACB subtends L. AOB at the centre O; and subtends L. APB at...
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School: A Monthly Record of Educational Thought and Progress, Volume 4

Ed - 1905 - 272 pages
...perpendicular to BC, then AB1 - AC1 = 2BC . DD'. (A) The angle which an arc subtends at the centre of a circle is double that which it subtends at any point on the remaining part of the circumference. (B) Draw a circle of radius 4 cm., and take a point 6.5 cm. from its centre. Construct a pair of tangents...
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Calendar

University of Allahabad - 1908 - 568 pages
...tangents at any point of a circle and the radius through the point are perpendicular to one another. If two circles touch, the point of contact lies on...of the circumference. Angles in the same segment of n circle are equal ; and, if the line joining two points subt- ads equal angles at two other points...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908 - 228 pages
...(Euc. III. 11, I2) 244 CHAPTER XII.— THE CIRCLE: ANGULAR PROPERTIES. Angular Properties. AC. 1. — The angle which an arc of a circle subtends at the...that which it subtends at any point on the remaining arc of the circumference . . . (Euc. III. 2O) 254 AC. 2. — Angles in the same segment of a circle...
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