Y by
Let two circles
and
meet at two distinct points
and
. Choose any line
through
, and let
meet
again at
(other than
) and meet
again at
. On
, let
be the midpoint of the minor arc
(i.e., the point on
such that
subtends the arc
), and on
let
be the midpoint of the minor arc
. Prove that
![\[
MN \parallel \text{(radical axis of } \omega_1, \omega_2).
\]](//latex.artofproblemsolving.com/6/6/4/6647f0f7182bdf5096ec5f2956a272803082f4f7.png)





















![\[
MN \parallel \text{(radical axis of } \omega_1, \omega_2).
\]](http://latex.artofproblemsolving.com/6/6/4/6647f0f7182bdf5096ec5f2956a272803082f4f7.png)
This post has been edited 1 time. Last edited by Arytva, Jun 6, 2025, 9:30 AM