2025 CGS PRELIMS P2 Q4

2025 CGS PRELIMS P2 Q4

Secondary 4
10 marks
2025 Crescent Girls' School Prelims A Math Paper 2

The diagram shows two chords \(AB\) and \(CD\) intersect at \(X\) such that angle \(CXB = 90^\circ\).

Given that \(AC = 5\text{ cm}\), \(BD = 12\text{ cm}\) and angle \(BDC = \theta\).

  1. Prove that \(AB = 5\cos\theta + 12\sin\theta\).[3]
  2. Express \(AB\) in the form \(R\cos(\theta - \alpha)\) where \(R > 0\) and \(\alpha\) is an acute angle.[4]
  3. Find the maximum length of \(AB\) and the corresponding value of \(\theta\). Hence state the radius of the circle.[3]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \(AB=5\cos\theta+12\sin\theta\) (b) \(AB=13\cos(\theta-67.4^\circ)\) (c) Maximum \(AB=13\text{ cm}\) when \(\theta=67.4^\circ\); radius \(=6.5\text{ cm}\).

Need help? Join our JC Math tuition classes.

Learn more