| André Darré - 1872
...which the sum of two opposite angles is 180°. 23. When a quadrilateral is described about a circle **the sum of one pair of opposite sides is equal to the sum of the other pair.** SECTION III. PROPORTIONAL LINES. 76. WHEN a line AB (Fig. 67) has been added to itself several times... | |
| Isaac Todhunter - 1874
...Article 254. Here s = 7, °-a=4, sb=4, sc=3, sd=3. Thus the area=^/^x"4 x 3 x 3 = 12. Since the sum of a **pair of opposite sides is equal to the sum of the other pair,** a circle may be inscribed in the quadrilateral. Let p denote the radins of this inscribed circle ;... | |
| George Albert Wentworth - 1879 - 196 pages
...Ex. 281. If the diagonals of a quadrilateral cut each other at right angles, the sum of the squares **of one pair of opposite sides is equal to the sum of the** squares of the other pair. Ex. 282. In a rhombus the sum of the squares of the two diagonals is equal... | |
| Great Britain. Civil Service Commission - 1880
...the line which touches the circle. Prove that if a quadrilateral be described about a circle, then **the sum of one pair of opposite sides is equal to the sum of the other pair.** (a.) CHEMISTRY. (NB — Of the seven subjects a, b, c, d, e,f, g, two are obligatory.) Time allowed,... | |
| Julius Petersen - Geometry, Modern - 1880 - 86 pages
...quadrilateral the diagonals are at right angles to each other. Prove that the sum of the squares on the **one pair of opposite sides is equal to the sum of the** squares on the other pair. 148. A circle passes through the centre C of another circle and touches... | |
| Julius Petersen - Geometry, Plane - 1880 - 73 pages
...quadrilateral the diagonals are at right angles to each other. Prove that the sum of the squares on the **one pair of opposite sides is equal to the sum of the** squares on the other pair. 148. A circle passes through the centre C of another circle and touches... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...arc BD - \ angle arc CA. QED THEOREM XXIII. 249. If a quadrilateral ~be circumscribed about a circle, **the sum of one pair of opposite sides is equal to the sum of the other pair.** Hypothesis. ABCD, a quadrilateral touching a circle in the points P, Q, R, S. Conclusion. AB + CD =... | |
| Samuel Constable - Geometry - 1882 - 203 pages
...vertex to the base : construct it. 34. If a quadrilateral circumscribe a circle, prove that the sura **of one pair of opposite sides is equal to the sum of the other pair.** 35. Draw a straight line cutting two given circles, so that the intercepted chords shall each be of... | |
| Mathematical association - 1884
...33. The diagonals of a quadrilateral intersect at right angles : shew that the sum of the squares on **one pair of opposite sides is equal to the sum of the** squares on the other pair. *34- ABC is an equilateral triangle and AD is perpendicular to BC : shew... | |
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