 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
 | Canada. Topographical and Air Survey Bureau - 1908 - 758 pages
...CD equal to the arc AE. Show that the segment BAE equals one quarter of the area of the circle. ~j. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the rectangles contained by pairs of opposite sides. 6. Construct a triangle having each of two angles... | |
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...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. D) relating to the rectangle contained by the diagonals of a quadrilateral inscribed in a circle. The Arabians made the improvement of using in place of the chord of an arc the sine, or half chord,... | |
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...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... | |
 | University of St. Andrews - 1900 - 670 pages
...opposite angles, show that these lines will intersect on the median from the vertex of the triangle. 4. The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides. If ABC be an equilateral triangle, and P any point on its circumscribing circle, prove that AP is equal... | |
 | 1870 - 964 pages
...the same circle. 10. Triangles which have the 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... | |
 | University of Bombay - 1907 - 940 pages
...rectangle contained by the perpendicular and the diameter of the circle described about the triangle. The 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... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1871 - 902 pages
...about the same circle. 10. Triangles which have 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... | |
 | University of Bombay - 1916 - 654 pages
...rectangle contained by the perpendicular acd the diameter of the circle described about tbe triangle. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of tbe rectangles contained by the two pain of opposite sides. The ratio of the areas of similar triangles... | |
 | University of Bombay - 1910 - 1080 pages
...rectangle contained by the perpendicular and the 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... | |
 | Actuarial Society of America - Insurance - 1917 - 480 pages
...equation whose roots are - and -• (6) If a : /3 = m : n show that mnb? = (m + «)2 o&. 8. The product of the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the products of the opposite sides. 9. ABCD is a parallelogram, O a point within it; through 0, lines MN,... | |
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