Question 9
Let \(ABC\) be a right-angled triangle with \(\angle A=90^\circ\), \(AB=c\), \(AC=b\). Let \(E\in AC\), \(F\in AB\) satisfy \(\angle AEF=\angle ABC\), \(\angle AFE=\angle ACB\). Let \(P,Q\in BC\) satisfy \(EP\perp BC\), \(FQ\perp BC\). Determine \(EP+EF+PQ\).