4 coplanar points

Geometry Level 3

Let there exist 3 coplanar points \(B\), \(C\), and \(D\) such that \(BC=5\) and \(CD=7\) and \(\angle BCD =\) \(120^\circ\). \(A\) is a point in the same plane that lies on the angle bisector of \(\angle BCD\). Then what should be the value of \(CA\) so that the points \(B\), \(A\) and \(D\) are collinear?

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