 | 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. 9. Solve... | |
 | Public schools - 1878 - 710 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... | |
 | 1879 - 636 pages
...the point of contact, and terminated by the circles, are divided in the same ratio at that point. 9. The rectangle contained by the diagonals of a quadrilateral...of the rectangles contained by its opposite sides. INSPECTORS, NATIONAL SCHOOLS, ALGEBRA. (OBLIGATORY.) Time allowed, 3 hours. 1. Find the value of —... | |
 | 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...of the rectangles contained by its opposite sides. INSPECTORS, NATIONAL SCHOOLS, IRELAND. ALGEBRA. (OBLIGATORY.) Time allowed, 3 hours. 1. Find the value... | |
 | 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... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 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 inscribed in a circle is equal to the sum of the two rectangles contained by the opposite sides. 105. If a perpendicular is drawn from the vertex of... | |
 | Oxford univ, local exams - 1880 - 396 pages
...drawn parallel to the base. 11. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 12. If a straight line stand at right angles to each of two straight lines at their point of intersection,... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...OA produced in a fixed point. 11. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. ALGEBEA. 1 . Show that the result is the same whether 2 -f- д/ 3 or 2 — v' 3... | |
 | George Shoobridge Carr - Mathematics - 1880
...base and the diameter of the circumscribing circle. VI. D. — Ptolemy's Theorem. The rectangle of the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles under the opposite sides. BOOK XL XI. 4. — A right line perpendicular to two... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...££.a*. §278 EA AC :.BA X AC = EA X AD. QED 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. J3 Let ABC D be any quadrilateral inscribed in a circle, AC and BD... | |
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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. Let ABCD be any quadrilateral inscribed in a circle... 
