2025 SAJC P1 Q11

The points \(A\), \(B\) and \(A'\) lie on a circle with center \(O\) such that \(\overrightarrow{OA}=\mathbf{a}\) and \(\overrightarrow{OB}=\mathbf{b}\). It is also given that the line segment \(AA'\) is a straight line that passes through \(O\) (see diagram).

1. Using a suitable scalar product, prove that \(\angle ABA'=90{}^\circ\).[4]
2. Express the area of \(\Delta ABA'\) in the form \(k|\mathbf{a} \times \mathbf{b}|\), where \(k\) is a real constant.[2]