2025 BVSS PRELIMS P2 Q6

2025 BVSS PRELIMS P2 Q6

Secondary 4
10 marks
2025 Bedok View Secondary School Prelims A Math Paper 2

The diagram shows two circles \(P\) and \(Q\) which intersect each other at \(F\) and \(G\). The line \(ABC\) is tangent to \(P\) and \(Q\) at \(B\) and \(C\) respectively. The line \(AED\) is tangent to \(P\) and \(Q\) at \(E\) and \(D\) respectively. \(EFC\) is a straight line.

  1. Prove that triangle \(ABE\) is similar to triangle \(ACD\).[4]
  2. Explain why a circle can be drawn to pass through \(BEDC\).[3]
  3. Prove that angle \(CBF\) = angle \(EDF\).[3]

Solution:

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Answer:\(\text{(a)}\hspace{0.5em}\triangle ABE\sim\triangle ACD\text{ by SAS.}\) \(\text{(b)}\hspace{0.5em}B,E,D,C\text{ are concyclic.}\) \(\text{(c)}\hspace{0.5em}\angle CBF=\angle EDF.\)

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