2025 AISS PRELIMS P1 Q6

2025 AISS PRELIMS P1 Q6

Secondary 4
9 marks
2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 1

The diagram shows a circle passing through the points \(P\), \(Q\) and \(R\). The point \(Q\) lies on the line \(RB\). \(AB\) is a tangent to the circle at \(P\). The points \(S\) and \(T\) lie on \(PR\) and \(PQ\) respectively. Given that \(AB\) is parallel to \(ST\), prove that

  1. triangle \(PST\) is similar to triangle \(PQR\),[3]
  2. \(PQ \times PT = PR \times PS\),[2]
  3. Determine if \(STQR\) is a cyclic quadrilateral.[4]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \(\triangle PST\sim\triangle PQR\). (b) \(PQ\times PT=PR\times PS\). (c) \(STQR\) is a cyclic quadrilateral.

Need help? Join our JC Math tuition classes.

Learn more