Triangle Drawn to a Circle
Given circle \(\Gamma\), point \(A\) is chosen outside of \(\Gamma\). Tangents \(AB\) and \(AC\) to \(\Gamma\) are drawn. \(K\) is a point on the circumference of \(\Gamma\) contained within \(ABC\). \(D\) is a point on \(AB\) and \(E\) is a point on \(AC\) such that \(DKE\) is a straight line and tangent to \(\Gamma\). If \(AB = 19\), what is the perimeter of triangle \(ADE\)?