 | Queensland. Department of Public Instruction - Education - 1916 - 244 pages
...Teacher of the Second Class. (THREE HOURS ALLOWED.) 1. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. 2. Areas of triangles of equal altitude are to one... | |
 | Alexander H. McDougall - Geometry - 1919 - 232 pages
...AC = rect. BD . DC + AD5. 15. Ptolemy's Theorem :— 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. This theorem is a particular case ofthat o/§ 16. ABCD is a quadrilateral... | |
 | Canada. Topographical and Air Survey Bureau - 1908 - 758 pages
...through D will bisect BC at right angles. 17 5. The rectangle contained by the diagonals of a convex quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by pairs of the opposite sides. 17 6. Inscribe a regular pentagon in a given circle. 17 7.... | |
 | Eli Maor - Pythagorean theorem - 2007 - 296 pages
...astronomy. There we find the following result, known as Ptolemy's theorem: The rectangle contained by the diagonals of any quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the pairs of opposite sides. To understand this cryptic statement, we must again remember... | |
 | Euclid - 452 pages
...injXtKOTijTos r<Sv a> r<3 KuVAu tvticiav). The theorem may be enunciated thus. The rectangle contained by the diagonals of any quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the pairs of opposite sides. I shall give the proof in Ptolemy's words, with the addition... | |
 | University of Bombay - 1910 - 1080 pages
...diameter of the circle described about the triangle. Tha rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by the two pairs of opposite sides. The ratio of the areas of similar triangles is equal... | |
 | 1870 - 964 pages
...same altitude are to one another as their bases. 11. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by ite opposite sides. ALGEBRA. Time allowed, 3 hours. 1. Reduce to their simplest forms... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1871 - 902 pages
...the same altitude are to one another as their bases. Hi 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. ALGEBRA. Time allowed, 3 hours. 1. Reduce to their simplest forms... | |
 | University of St. Andrews - 1900 - 670 pages
...intersect on the median from the vertex of the triangle. 4. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. If ABC be an equilateral triangle, and P any point... | |
 | 1874 - 748 pages
...prove that BD : DA : : CE : EA. 10. 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. ALGEBRA. Time allowed, 3 hours. 1. Prove |(1+2л;-За;2)2-(1-2а;+За;2)2|2=16лг2(... | |
| |
The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides. 
