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" In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides. "
Wentworth & Hill's Exercise Manuals: Geometry - Page 64
by George Albert Wentworth - 1884
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...of the opposite sides. (III. 64) and (Ex. 23.) 141. In any quadrilateral ABCD inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides ; that is, AC.DB = AD.BC + AB.DC. (Make the angle DAE = BAC, and prove that AD.BC =AC.DE, and AB.DC...
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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - Geometry - 1872 - 102 pages
...joining the centres of the diagonals. 677. In any quadrilateral which may be inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. 6Y8. In any triangle the rectangle of two sides is equivalent to the rectangle of the perpendicular...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...joining the centres of the diagonals. 677. In any quadrilateral which may be inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. 678. In any triangle the rectangle of two sides is equivalent to the rectangle of the perpendicular...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...of the opposite sides. (III. 64) and (Ex. 23.) 141. In any quadrilateral ABCD inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides ; that is, AC.DB = AD.BC + AB.DC. (Make the angle DAE=BAC, and prove that AD.BC=AC.DE, and AB.DC -=...
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A Treatise on Special Or Elementary Geometry: In Four Parts ..., Part 3

Edward Olney - Geometry - 1872 - 96 pages
...FIG. 381. squares of the diagonals. 252 677. In any quadrilateral which may be inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. 678. In any triangle the rectangle of two sides is equivalent to the rectangle of the perpendicular...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...points where they meet the circumferences, and prove that the A thus formed are similar. 238. In an inscribed quadrilateral, the product of the diagonals...to the sum of the products of the opposite sides. HINT. Draw DE, making Z CDE=ZADB. The A ABD and CDE are similar. Also the A BCD and ADE are similar....
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...altitude upon the third side. If AC, BC are taken as the two sides, draw the diameter CE, and join EB. 17. In every inscribed quadrilateral the product of...quadrilateral. In AC take a point E such that Z EDC= Z ADB. A ADB and ODE are similar; also, the A BCD and ADE. From these triangles obtain equations involving...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...altitude upon the third side. If AC, BCare taken as the two sides, draw the diameter CE, and join EB. 17. In every inscribed quadrilateral the product of...Let ABCD be the quadrilateral. In AC take a point .Esuch that Z EDC= Z ADB. A ADB and CDE are similar; also, the A BCD and ADE. From these triangles...
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...proportionally by the circumference of the smaller. 381. In any quadrilateral inscribed in a circle, the product of the diagonals is equal to the sum of the products of the opposite sides. Sug. From one vertex draw a line to the opposite diagonal, making the angle formed by it and one side...
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A History of Mathematics

Florian Cajori - Mathematics - 1893 - 478 pages
...circle — a limitation which he omits to state. Among these is the proposition of Ptolemaeus, that the product of the diagonals is equal to the sum of the products of the opposite sides. The Hindoos were familiar with the calculation of the areas of circles and their segments, of the length...
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