easiest one yet.

Triangle \(ABC\) has the largest angle at \(A\), let \(\omega\) be the circle that passes through \(A,B\) and also tangent to \(AC\). Denote \(D,E\) the midpoint of major arcs \(ABC,ACB\), and let \(\Omega\) be the the circle that passes through \(A,E\) and also tangent to \(AD\). Suppose \(\omega \cap \Omega=A,F\), prove that \(AF\) bisects \(BAC\).

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