 | Bombay (India : State). Board of Education - Education - 1851 - 768 pages
...lines from a point within a square to the angles, to construct it ? 10. If a perpendicular be let fall from the intersection of the diagonals of a quadrilateral inscribed in a circle upon the third diagonal, it will pass through the centre ? 1 1 . Given the segments into which the... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...of the Proposition proved in Art. 37, 4°. 4°. "We saw in Art. 40, 5°, that a line passing through the intersection of the diagonals of a quadrilateral, inscribed in a circle, and parallel to the third diagonal, gives equal intercepts between that point and either pair of opposite... | |
 | Mathematics - 1865 - 132 pages
...the pressure on the upper sphere for any position of the spheres. 1705. (Proposed by H. MURPHY.) — If from the intersection of the diagonals of a quadrilateral...inscribed in the given one, the one of least perimeter. Solution by ABCHEB STANLEY; J. DALE ; E. FITZGERALD; and others. ABCD being the given quadrilateral... | |
 | Bombay (India : State). Board of Education - Education - 1851 - 764 pages
...the point K is determined ; .-. DOPM is the required square. 10. Q. If a perpendicular be let fall from the intersection of the diagonals of a quadrilateral inscribed in a circle upon the third diagonal, it will past through the centre. A. Inscribe a square ADBC in the circle ;... | |
 | Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...PRQ are equal and on the same side of PQ : prove that R lies on a fixed circle. 20. From the point of intersection of the diagonals of a quadrilateral inscribed in a circle perpendiculars are let fall on the sides : prove that the sum of two opposite angles of the quadrilateral formed by... | |
 | University of Madras - 1876 - 580 pages
...than the base of the other. II. The angles in the same segment of a circle are equal to one another. From the intersection of the diagonals of a quadrilateral inscribed in a circle, perpendiculars are let fall upon the sides ; prove that the semi-sum of two opposite angles of the quadrilateral formed... | |
 | Edinburgh Mathematical Society - Mathematics - 1894 - 284 pages
...that as it holds when the rays are produced backwards, it immediately leads to such theorems as : 1 . The intersection of the diagonals of a quadrilateral inscribed in a circle is upon the polar of the intersection of the opposite sides. 2. The theorem proposed by Mr James Taylor... | |
 | W. J. C. Miller, D. Biddle - Mathematics - 1901 - 128 pages
...the pressure on the upper sphere for any position of the spheres. 1705. (Proposed by H. MUBPHY.) — If from the intersection of the diagonals of a quadrilateral...inscribed in the given one, the one of least perimeter. Solution by AHCHEE STANLEY ; .1. DALE ; E. FITZGEBALD; and others. ABCD being the given quadrilateral... | |
 | Dublin city, univ - 1865 - 348 pages
...given lines AB, AC is an harmonic mean between the areas of the triangles, BOA, CO A. MR. LESLIE. 9. If from the intersection of the diagonals of a quadrilateral inscribed in a circle perpendiculars be dropped on the sides, the quadrilateral formed by joining their feet is, of all quadrilaterals inscribed... | |
 | Marcel Berger - Mathematics - 2009 - 416 pages
...of P. Also if and only if the circle passing through m, m',m" contains the vertex of P. 17.9.18.3. The intersection of the diagonals of a quadrilateral inscribed in a circle and circumscribed around a parabola belongs to the directrix of the parabola. 17.9.19. Consider two... | |
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If from the intersection of the diagonals of a quadrilateral inscribed in a circle perpendiculars be... 