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" Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. "
Science Examination Papers - Page 248
by Great Britain. Education Department. Department of Science and Art - 1899
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...perpendicular and the diameter of the circle described about the triangle. . . . . . . . . . . 240 D. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. . , 240 E. If a segment of a circle be bisected,...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...equal to the product of its three sides divided by twice the diameter of the circumscribed circle. 104. The rectangle contained by the diagonals of a quadrilateral...equal to the sum of the two rectangles contained by the opposite sides. 105. If a perpendicular is drawn from the vertex of a triangle ABC, to the base...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...other ; BA AD EA AC -. BA X AC = EA XAD. 278 PROPOSITION XX. THEOREM. 301. The product of the two diagonals of a quadrilateral inscribed in a circle is equal to the sum of the products of its opposite sides. Let ABC D be any quadrilateral inscribed in a circle, AC and BD its...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...AB:AE::AD:AC; and hence AB x AC = AE x AD. Therefore, in any triangle, etc. PROPOSITION XXXII. THEOREM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equivalent to the sum of the rectangles of the opposite sides. I.et ABCD be any quadrilateral inscribed...
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Dublin examination papers

Dublin city, univ - 1878 - 498 pages
...roots are the solutions of the equations ax + 6y = c, ax + $y = y. MR. BCHNSIDE. 7. The rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite sides ? 9. Describe a circle touching two right lines and a given circle....
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Exercises on Euclid and in modern geometry, New ed., revised

James McDowell - 1878 - 312 pages
...under the whole produced bisector and its produced part ................ 61 93. The rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under its opposite sides (VI. D) ................ 61 94. If perpendiculars be drawn from...
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An elementary manual of coordinate geometry and conic sections

James White - Conic sections - 1878 - 160 pages
...Then there are two similar triangles formed, as in previous proposition. XXVIII. The rectangle under the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles under the opposite sides.. XXIX. If from any point on the circumference of a circle perpendiculars...
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Annual Report

Public schools - 1878 - 716 pages
...prove a theorem equivalent to the expression (a +b) x (a— S) =a'-*. ' () 5. Find the value of the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. (*) 6. A circular fish-pond covering half an acre, is to be dug in a garden ; what must be the length...
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Parliamentary Papers, Volume 22

Great Britain. Parliament. House of Commons - Great Britain - 1879 - 632 pages
...the point of contact, and terminated by the circles, are divided in the Fame ratio at that point. 9. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. INSPECTORS, NATIONAL SCHOOLS, IRELAND. ALGEBRA. (OBLIGATORY.)...
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Crumbs swept up. Complete ed

Thomas De Witt Talmage - 1879 - 216 pages
...turned into a hypotenuse, and gets his body so thoroughly mixed up and out of place, that he proves that the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equivalent to the sum of the rectangles of the opposite sides ; and winds np his mathematical exercises...
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