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" The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair. "
Proceedings of the Edinburgh Mathematical Society - Page 50
by Edinburgh Mathematical Society - 1894
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Elements of geometry, with ... trigonometry

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...
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Plane trigonometry. Key

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 ;...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

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...
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Report of Her Majesty's Civil Service Commissioners, Together ..., Volume 24

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,...
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Text-book of Elementary Plane Geometry

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...
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Text-book of Elementary Plane Geometry

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...
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Elements of Geometry

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 =...
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Geometrical Exercises for Beginners

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...
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The elements of plane geometry, Volume 1

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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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...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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