| John Hind - Trigonometry - 1855 - 328 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 - 344 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
...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 - 302 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 - 148 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 - 536 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 - 104 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 - Conic sections - 1881 - 384 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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