Читать онлайн «Элементы геометрии треугольника»

НЕСКОЛЬКО ЗАМЕЧАТЕЛЬНЫХ ПРЯМЫХ SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN 1)N—S —M —I,гдеS— точка Шпикера — центр вписанной окружности се- рединного треугольника. IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN GlG lG lG lG lG lGlG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lG lGlG lG lG lG lG lG l NlNlNlNlNlNlNlNlNlN lN lN lN lNlNlNlNlNlNlNlNlNlNlNlN lN lN lN lNlNlNlNlNlNlNlNlN l 2) O — Gl=Fl(G)—I — Nl=Fl(N), где Fl — изого- нальное сопряжение. MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH 3) Hm =Fm(H)—M — L=Fl(M), где Fm —изото- мическое сопряжение. HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN ImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImIm GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG GcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGcGc 4)Hm — N —Im=Fm(I)— Gc =Fc(G)—G,гдеFc — изоциркулярное преобра- зование. ISBN 5 90457 048 8 9 785904 570484 Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm Lm ImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImImIm SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL 5) Lm =Fm(L)—Im — S. F MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM GlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGlGl GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 6) M—Gl—F,гдеF—точка Фейербаха — точка каса- ния вписанной окружно- сти и окружности девяти точек. FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH NlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNlNl NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN 7)H—Nl—F. Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm Hm HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl (Fm (H)) Fl (Fm (H)) Fl (Fm (H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl (Fm (H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl (Fm (H)) Fl (Fm (H)) Fl (Fm (H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) Fl(Fm(H)) EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 8) O—M—E—H—Fl(Fm (H)) (прямая Эйлера).