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" If any chord of a circle be produced equally both ways, and tangents to the circle be drawn on opposite sides of it from its extremities, the line joining the points of contact bisects the given chord. "
382 exercises, solved, upon the 3rd, 4th, 5th, and 6th books of Euclid - Page 81
by Patrick M. Egan - 1883
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...the straight lines joining the opposite points of intersection will both pass through the centre. 46. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. 47. When the vertical angle and the sum of the sides of a plane triangle are given, prove that the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...points without the circle to the point of intersection, shall be perpendicular to the diameter. 41. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. 42. AB is a chord, and AD is a tangent to a circle at A. DPQ any secant parallel to AB meeting the...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...points without the circle to the point of intersection, shall be perpendicular to the diameter. 41. If any chord of a circle be produced equally both...tangents to the circle be drawn on opposite sides of it Irom its extremities, the line joining the points of contact bisects the given chord. 42. AB is a chord,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...points without the circle to the point of intersection, shall be perpendicular to the diameter. 41. If any chord of a circle be produced equally both...tangents to the circle be drawn on opposite sides of it Irom its extremities, the line joining the points of contact bisects the given chord. 42. AB is a chord,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...point without the circle to the point of intersection, shall be perpendicular to the diameter. 46. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. 47. AB is a chord, and AD is a tangent to a circle at A. DPQ any secant parallel to AB meeting the...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...the straight lines joining the opposite points of intersection will both pass through the centre. 48. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. Arithmetical Questions. 1. From a given point, A, a straight line is drawn, cutting a circle at points...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...points without the circle to the point of intersection, shall be perpendicular to the diameter. 41. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. 42. AB is a chord, and AD is a tangent to a circle at A. JDPQ any secant parallel to AB meeting the...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...the straight lines joining the opposite points of intersection will both pass through the centre. 48. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. Arithmetical Questions. 1. From a given point, A, a straight line is drawn, cutting a circle at points...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...points without the circle to the point of intersection, shall be perpendicular to the diameter. 41. If any chord of a circle be produced equally both...joining the points of contact bisects the given chord. 42. AB is a chord, and AD is a tangent to a circle at A. DPQ any secant parallel to AB meeting the...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...straight lines joining the opposite points of intersection will both pass through the centre. 122. If any chord of a circle be produced equally both ways and tangents to the circle be drawn oh opposite sides of it from its extremities, the line joining the points CHAPTER XV. MAXIMA AND MINIMA....
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