Question 11
Consider a right-angled triangle \(ABC\) with \(\angle A=90^\circ\), \(AB=c\) and \(AC=b\). Let \(P\in AC\) and \(Q\in AB\) satisfy \(\angle APQ=\angle ABC\) and \(\angle AQP=\angle ACB\). Calculate \(PQ+PE+QF\), where \(E,F\) are the perpendicular projections of \(P,Q\) onto \(BC\), respectively.