2026 CSS P2 Q9

\(A\), \(B\), \(C\) and \(D\) are points on the circumference of a circle with centre \(O\).

\(AE\) is a tangent to the circle at \(A\) and \(OE\) is a straight line that passes through the circle at point \(B\).

Angle \(BCD\) is \(98^\circ\) and angle \(OAD\) is \(30^\circ\).

1. Find the following angles.
   1. Angle \(BAD\).[1]
   2. Angle \(BOA\).[1]
   3. Angle \(OEA\).[1]
   4. Explain why a semicircle with \(OE\) as diameter passes through point \(A\).[1]
2. \(ABCD\) is a rhombus and \(RD=SC\).
   \(SCB\), \(DCR\) and \(AQR\) are straight lines.
   The diagram is not drawn to scale.
   Prove that triangles \(SCD\) and \(RDA\) are congruent.[3]