 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...The diagonals of a quadrilateral are perpendicular to each other ; prove that the sum of the squares of one pair of opposite sides is equal to the sum of the squares of the other pair. Ex. 429. The legs of a right triangle are a and b, and the perpendicular... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...which subtends a right angle at the centre. V 11. In any quadrilateral circumscribed about a circle, the sum of one pair of opposite sides is equal to the siim of the other pair. V 12. Any parallelogram which can be circumscribed about a circle, must be... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...to be inscribed in the polygon. 396. EXERCISE. If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. Suggestion. Use § 393. 397. EXERCISE. From the point A two tangents AB and AC are drawn to the circle... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...quadrilateral is such that its diagonals 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 of opposite sides. 6. If O is the point of intersection of the perpendiculars... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...to be inscribed in the polygon. 396. EXERCISE. If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. Suggestion. Use § 393. 397. EXERCISE. From the point A two tangents AB and AC are drawn to the circle... | |
 | James McMahon - Geometry, Plane - 1903 - 382 pages
...pair of opposite sides is equal to the sum of the other pair. 9. If a convex quadrangle is such that the sum of one pair of opposite sides is equal to the sum of the other pair, then a circle may be inscribed in it. TWO CIRCLES t 81. Definitions. Two circles are said to intersect... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...which subtends a right angle at the centre. 11. In any quadrilateral circumscribed about a circle, the sum of one pair of opposite sides is equal to the mm of the other pair. 12. Any parallelogram which can be circumscribed about a circle, must be equilateral.... | |
 | George Clinton Shutts - 1905 - 260 pages
...If 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. SUPPLEMENTARY PROPOSITIONS. Ex. 433. (§ 96.)* The angle formed by the bisectors... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...arc a'. .-. the chords are equal by § 243.] 267 If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. [§ 254.] 268 The median of a circumscribed trapezoid is equal to one-fourth of the perimeter. [Ex.... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...a'. . -. the chords are equal by § 243. ] 267 If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. [§ 254.] 268 The median of a circumscribed trapezoid is equal to one-fourth of the perimeter. [Ex.... | |
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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. 
