 | 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-)... | |
 | 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... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...CD may 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... | |
 | Charles Taylor - Conic sections - 1872 - 121 pages
...the four 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... | |
 | S. A. Renshaw - Conic sections - 1875 - 222 pages
...the 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... | |
 | 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... | |
 | Charles Taylor - Conic sections - 1880 - 152 pages
...the four 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... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...contact are 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... | |
 | Charles Taylor - Mathematics - 1881 - 512 pages
...contact arc 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... | |
 | John James Milne - 1885 - 392 pages
...sin 1C = 4(Д2 + /P) sin A sin B sin С, R being the radius of the circum-circle. 7. A conic passes through the centres of the four circles which touch the sides of a triangle. Prove that the locus of its centre is the circumscribing circle. PAPER XIX. 2. Solve the... | |
| |
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. 
