2025 GESS PRELIMS P1 Q21

The diagram shows a circle \(ABCD\) with centre \(O\) and \(BD\) passing through \(O\). \(AC\) intersects \(BD\) at \(E\). Angle \(ACB=67^\circ\) and angle \(DAC=24^\circ\).

1. Prove, stating your reasons clearly, that \(\triangle AED\) is similar to \(\triangle BEC\).[2]
2. Given that \(AE=3.5\text{ cm}\), \(CE=4\text{ cm}\), and \(DE=2\text{ cm}\), calculate the length of \(EB\).[2]
3. Calculate, as a fraction, the numerical value of the ratio \(\dfrac{\text{minor arc length}\hspace{0.5em}AD}{\text{minor arc length}\hspace{0.5em}BC}\).[2]