2025 DSS PRELIMS P2 Q6

The diagram shows a circle \(ABCD\), centre \(O\). \(AT\) and \(CT\) are tangents to the circle. Angle \(ATC=32^\circ\) and angle \(ACB=38^\circ\).

1. Find angle \(ADC\). Give a reason for each step of your working.[3]
2. Determine if \(OC\) is parallel to \(AB\). Give a reason for each step of your working.[3]
3. The radius of the circle is \(10\text{ cm}\). Calculate the area of the shaded region.[4]