Posted: Wed Mar 30, 2005 9:52 am    Post subject:

Since your question is too concise and seems to have typos, I would like to rewrite the problem:

Problem

and are two chords of a circle. The circles with diameter and respectively meet at and . Lines and meet at . Prove that are collinear. Indeed there is a more general result:

and are two chords of a circle. Two circles having chords and respectively meet at and . Lines and meet at . Prove that are collinear.

Actually this is a well-known theorem: The radical axes of three circles are concurrent.