ssible.We consider case , but this ,with , gives ,giving , again not possible.The last case and the only possibility is .But we have implying . Hence we must have , and we are done!Р6.设锐角三角形的外接圆为,是圆的一条切线.记切线关于直线,和的对称直线分别为,和.证明:由直线,和构成的三角形的外接圆与圆相切.РDenote the intersections of and , respectively; the intersections of 3 lines .РLet be the point of contact of and ; be the reflections of wrt be the Miquel point of pleted quadrilateral .РWe have the distances from to are equal so is the bisector of angle РWe get РOn the other side, let be the projections of onto then passes through the midpoint of . Р, which follows that are concyclic. We get РFrom and we obtain . Similarly with РSo РTherefore РConstruct a tangent of . We will show that is also a tangent of iff .РBut РHence is true. We are done.
全文预览
