Problems: 4421–4430

摘要

Let distinct points A, B, C on a rectangular hyperbola H be such that ∠BAC =90?. A point M of H, other than A, B, C, is called good if the triangles MAB andMAC have the same circumradius. Show that either infinitely many M are goodor a unique M is good. Characterize the triangle ABC in the former case and findM and the common circumradius in the latter one.