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" In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector. "
Plane and Solid Geometry - Page 174
by Isaac Newton Failor - 1906 - 418 pages
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Chapters on the Modern Geometry of the Point, Line, and Circle ..., Volume 1

Richard Townsend - Geometry, Modern - 1863 - 328 pages
...therefore pd = bc, qd — ca, rd = ab, and therefore generally — In every triangle the product of any two sides is equal to the product of the diameter of the circumscribing circle into the perpendicular on the third side from the opposite vertex. This property...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...parallelogram, the diagonals bisect each other, and the distance EF is zero. PROPOSITION XX.— THEOREM. 65. In any triangle, the product of two sides is equal...product of the diameter of the circumscribed circle by the perpendicular let fall upon the tidrd side from the vertex of the opposite angle. Let AB, AC,...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...are similar, and give AB : AE = AD : AC, whence, AB X AC = AE X AD. PROPOSITION XXI.— THEOREM. 66. In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...are similar, and give AB : AE = AD : AC, whence, AB X AC = AE X AD. PROPOSITION XXI.—THEOREM. 66. In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...are similar, and give AB : AE = AD : AC, whence, AB X AC = AE X AD. PROPOSITION XXI.— THEOREM. 66. In any triangle, the product of two sides is equal to the produd of the segments of the third side formed by the bisector of the opposite angle plus the square...
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 888 pages
...drawn, the angent is a mean proportional between the whole secant and its external segment. 'rove that in any triangle the product of two sides is equal to the product of the segnents of the third side formed by the bisector or the opposite angle together with the qnaru of...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...which cuts off upon the line the greater distance from the foot of the perpendicular. Corollaries. 2. In any triangle the product of two sides is equal...product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. 3. Two sides...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...the above equality BD XD С for ED XAD, then BAX AC = ВD X DC + Tff. PROPOSITION XIX. THEOREM. 300. In any triangle the product of two sides is equal...product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. Let ABC be...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...equality BDXD С for EDXAD, then BAX AC = BDX DC+Tl?. PROPOSITION XIX. THEOREM. 300. In any triangle ihe product of two sides is equal to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. Let ABC be...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...Show that as PA is to PK so is С F to CE, and so also is PH to PB. PROPOSITION XVIII. THEOREM. 299. In any triangle the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite anyle together with the square of...
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