Circle Tangent Lengths
Given circle \(\Gamma\), point \(A\) is chosen outside of \(\Gamma\). Tangents \(AB\) and \(AC\) to \(\Gamma\) are drawn, such that \(B\) and \(C\) lie on the circumference of \(\Gamma\). \(K\) is a point on the circumference of \(\Gamma\) contained within \(ABC\). Let \(D, E\) and \(F\) be the foot of the perpendiculars from \(K\) to \(BC, AC\) and \(AB \), respectively. If \(KF = 20 \) and \(KE = 28 \), what is \(KD^2\)?