Question 12
Let \(A\) lie inside the acute angle \(xOy\). An arbitrary circle \(\omega\) through \(O,A\) meets rays \(Ox,Oy\) again at \(B,C\), respectively. Let \(M\) be the midpoint of \(BC\). Prove that \(M\) always lies on a fixed line as \(\omega\) varies through \(O,A\).