 | John Hind - Trigonometry - 1855 - 540 pages
...ОТ «OS В and cot .V (B -A) = - : — =3- . m sin B 53. Iff/,, d2, i/3, dt be the distances, of the centres of the four circles which touch the sides of a triangle, from that of the circumscribed circle, then d,- + ¿г' + d,' + dt' = 4K2 + 2A(r,+r2 + r3-i-) = 12/2*.... | |
 | Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...is produced to meet the circle in E : prove that AE is bisected inD. 33. The straight lines joining the centres of the four circles which touch the sides of a triangle are bisected by the circumscribed circle : also the middle point of the line joining any two of the... | |
 | W. J. C. Miller - Mathematics - 1867 - 120 pages
...I. Solution by the PBOPOSKB. 1. To show that the foci of the two imaginary parabolas drawn through the centres of the four circles which touch the sides of a given triangle ABC coincide with the circular points at infinity. The two parabolas which pass through... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...be of constant magnitude, the locus of P is a rectangular hyperbola. 19. Every conic passing through the centres of the four circles which touch the sides of a triangle, is a rectangular hyperbola. 20. Ellipses are inscribed in a given parallelogram, shew that their foci... | |
 | Charles Taylor - Conic sections - 1872 - 121 pages
...common points of two rectangular hyperbolas is itself a rectangular hyperbola. 206. A conic through the centres of the four circles which touch the sides of a triangle is a rectangular hyperbola, and its centre is on the circumscribing circle. 207. Any chord of a rectangular... | |
 | S. A. Renshaw - Conic sections - 1875 - 222 pages
...circle circumscribing CTQ touches the ordinate QV conjugate to CP. 101. — Every Conic passing through the centres of the four circles which touch the sides of a triangle is a rectangular Hyperbola. 102. — The foci of Ellipses inscribed in a given parallelogram lie on... | |
 | Joseph Wolstenholme - Mathematics - 1878 - 538 pages
...is produced to meet the circle in E : prove that AE is bisected in D. 56. The straight lines joining the centres of the four circles which touch the sides of a triangle are bisected by the circumscribed circle ; also the middle point of the line joining any two of the... | |
 | Charles Taylor - Conic sections - 1880 - 152 pages
...common points of two rectangular hyperbolas is itself a rectangular hyperbola. 216. A conic through the centres of the four circles which touch the sides of a triangle is a rectangular hyperbola, and its centre is on the circumscribing circle. 217. On opposite sides... | |
 | Charles Taylor - Mathematics - 1881 - 488 pages
...or supplementary to the angles which they subtend at the centre. • i 477. If a conic pass through the centres of the four circles which touch the sides of a triangle it must be a rectangular hyperbola, and its centre will lie on the circumscribed circle of the triangle.... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...equal or supplementary to the angles which they subtend at the centre. 477. If a conic pass through the centres of the four circles which touch the sides of a triangle it must be a rectangular hyperbola, and its centre will lie on the circumscribed circle of the triangle.... | |
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The six straight lines. joining two and two the centres of the four circles which touch the sides of a triangle pass each through one of the vertices of the triangle. 
