 | Mathematics - 1862 - 428 pages
...respectively to the sides of the triangle has a fourth tangent tchich is also a common tangent to two of the four circles which touch the three sides of the triangle. TRIANGULAR SYSTEMS OF CIRCLES. 20. If ABC, A'B'C' be two Poncelefs triangles inscribed •in a circle... | |
 | Robert Henry Wright - Coordinates, Trilinear - 1865 - 174 pages
...intersection of the perpendiculars let fall from each angular point of the triangle on the opposite side. 152. If a rectangular hyperbola be so described that each...it of the opposite side, it will pass through the centers of the four circles which touch the three sides of the triangle. 153. To find the direction... | |
 | Arthur McCracken Harding, George Walker Mullins - Geometry, Analytic - 1924 - 340 pages
...bisectors in Exs. 31 and 32 meet in a point four times by threes. Find the center and radius of eaeh of the four circles which touch the three sides of the triangle. Check by the formula 1/r = 1/ri + l/r2 + l/ra. 37. Show that the three perpendiculars in Ex. 33 meet... | |
 | Mathematics - 1862 - 290 pages
...P, Q, R, and G are the centres of the escribed and inscribed circles of the triangle DEF. Therefore if a rectangular hyperbola be so described that each...opposite side, it will pass through the centres of the inscribed and escribed circles of the triangle j and its centre will be on the circumscribing circle.... | |
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In other words, if a rectangular hyperbola be so described that each angular point of a given triangle is the pole, with respect to it, of the opposite side, it will pass through the centres of the four circles which touch the three sides of the triangle. 