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 248by Great Britain. Education Department. Department of Science and Art - 1899Full view - About this book
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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.)... | |
| 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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