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" If } from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment. "
Plane Geometry - Page 146
by Arthur Schultze, Frank Louis Sevenoak - 1911 - 233 pages
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...that is, the rectangles of each secant and its external segment arc equal. PROPOSITION XXX. THEOREM. If from a point without a circle, a tangent and a secant are drawn, the secant terminating in the concave arc, the tangent is a t1tfan proportional between...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...secant and the external segment is constant in whatever direction the secant is drawn. 166. Theorem. If from a point without a circle a tangent and a secant are drawn, the tangent is a mean proportional between the entire secant and the external segment. PROBLEMS....
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...secant and the external segment is constant in whatever direction the secant is drawn. 166. Theorem. If from a point without a circle a tangent and a secant are drawn, the tangent is a mean proportional between the entire secant and the external segment. PROBLEMS....
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...= 20, and CD = 24, find the lengths of CP and DP when CD bisects AB. Proposition 3O. Theorem. 339. If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and the external segment. Hyp. Let PC and PB be a tangent...
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Examination Papers for the Academic Year ...

Examinations - 1893 - 408 pages
...circles angles at the center are in the same ratio as their intercepted arcs. (Two cases.) 8 6 Prove that if from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and the external segment. 5 7 Solve the following and...
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Examinations Papers

1893 - 762 pages
...There was one universal shout for Nature." PUEE MATHEMATICS.— PAST I. The Board of Examiners. 1. If from a point without a circle a tangent and a secant be drawn, then the rectangle contained by the whole secant and the part of it without the circle shall be equal...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...exterior segment is equal to the product of the other secant and its exterior segment. 235. Theorem. If from a point without a circle a tangent and a secant are drawn to the circle, the tangent is a mean proportional between the entire secant and its exterior...
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...opposite A : PB', opposite A'. 274 Whence PA x PB' = PBxPA'. 250 QED PROPOSITION XVII. THEOREM 321. If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment. GIVEN — a fixed point P outside...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...opposite A : PB', opposite A'. 274 Whence PAxPB' = PBxPA'. 2 50 QED PROPOSITION XVII. THEOREM 321. If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment. GIVEN — a fixed point P outside...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...A : PB', opposite A'. 261 Whence PA x PB' = PB x PA' 237 f QED PROPOSITION XVII. THEOREM 30!). If from a point without a circle a tangent and a secant arc drawn, the tangent is a mean proportional between tlie whole secant and its external segment. GIVEN...
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