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 120by University of Calcutta - 1907Full view - About this book
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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