2025 PHS PRELIMS P1 Q23

In triangle \(ABC\), \(AB=40\text{ cm}\), \(BC=22\text{ cm}\), and \(AC=26\text{ cm}\). \(P\) lies on \(BC\) produced, with \(CP=10\text{ cm}\) and \(AP=24\text{ cm}\).

1. Explain why angle \(APB\) is a right angle.[1]
2. Express as a fraction in lowest terms
   1. \(\tan\angle ABP\),[1]
   2. \(\cos\angle ACB\).[1]
3. A circle passes through \(A\), \(P\) and \(B\). John says its radius is \(16\text{ cm}\). Do you agree? Explain.[2]