 Plane geometry (2 hours).— Any three points A', B', C, are taken on the sides BC, CA, AB, respectively, of a triangle ABC. Prove that— (1) the circles circumscribed about the triangles A'B'C, B'C'A. C'A'B meet in a point; (2) the centers of these...  Modern Geometry - Page 43by Charles Godfrey, Arthur Warry Siddons - 1912 - 168 pagesFull view - About this book
 | Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...in any other point than A, it is at right angles to the diameter through A. 7. If points X, Y, Z be taken on the sides BC, CA, AB respectively of a triangle ABC, prove that the circles circumscribed about the triangles A YZ. BZX, CXY meet in a point. 8. Prove that... | |
 | United States. Office of Education - Agricultural colleges - 1917 - 1336 pages
.... Ausbach, C. Brügel u. Sohn, 1894. Plane geometry (2 hours).— Any three pointa A', B', C', are taken on the sides BC, CA, AB, respectively, of a triangle ABC. Prove that— (1) the circles circumscribed about the triangles A'B'C, B'C'A. C'A'B meet in a point;... | |
 | Alexander Caswell Ellis - Education - 1917 - 1098 pages
...tmuMiamlaUendSrS-ltaS). Anabach, C. Brdgel u. Bonn, 1894. Plane geometry (2 hours).— Any three points A', B', C', are taken on the sides BC, CA, AB, respectively, of a triangle ABC. Prove that(1) the circles circumscribed about the triangles A'B'C, B'C'A, C'A'B meet in a point; (2)... | |
 | Raymond Clare Archibald - Mathematics - 1918 - 310 pages
...the linear relation between X and x. Plane geometry (2 hours). — Any three points A', B', C', are taken on the sides BC, CA, AB, respectively, of a triangle ABC. Prove that— (1) the circles circumscribed about the triangles A'B'C, B'C'A, C'A'B meet in a point;... | |
 | Arthur Warry Siddons, Reginald Thomas Hughes - Geometry - 1926 - 202 pages
...sides, then MN is of constant length and touches a fixed circle. Ex. 58. Three points, P, Q, R, are taken on the sides BC, CA, AB respectively of a triangle ABC. Show that the circles which circumscribe the triangles QAR, RBP, PCQ meet at a point O. Show also that the angle BOC is equal... | |
 | Education - 1917 - 964 pages
...express the linear relation between X and x. Plane geometry (2 hours).— Any three points A', B', C, are taken on the sides BC, CA, AB, respectively, of a triangle ABC. Prove that— (1) the circles circumscribed about the triangles A'B'C, B'C'A. C'A'B meet in a point;... | |
 | Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - Geometry - 1963 - 198 pages
...ABC, perpendiculars PL, PM, PN are drawn to the sides. Prove that the rectangles PL . MM, PM . NL, PN . LM are proportional to the sides BC, CA, AB....PQR is similar to ABC show that this point is the orthooentre of PQR and the ciroumcentre of ABC. Ex. 164. A straight line AB of constant length has... | |
 | 480 pages
...sides, then MN is of constant length and touches a fixed circle. Ex. 68. Three points, P, Q, R, are taken on the sides BC, CA, AB respectively of a triangle ABC. Show that the circles which circumscribe the triangles QAR, RBP, PCQ meet at a point O. Show also that the angle BOC is equal... | |
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