2025 SJI PRELIMS P2 Q6

2025 SJI PRELIMS P2 Q6

Secondary 4
8 marks

\(ABCD\) is a circle with centre \(O\). \(F\) is the midpoint of chord \(AD\), \(BF\) passes through \(O\), \(E\) is the intersection of \(BD\) and diameter \(AC\), and angle \(DBC=45^\circ\).

  1. Prove that triangles \(ABF\) and \(DBF\) are congruent, giving reasons.[2]
  2. Find, giving reasons,
    1. angle \(DAC\),[1]
    2. angle \(DCA\),[1]
    3. angle \(AOB\),[2]
    4. angle \(AED\).[2]

Solution:

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Answer:(a) congruent (SAS) (b)(i) \(45^\circ\) (ii) \(45^\circ\) (iii) \(135^\circ\) (iv) \(67.5^\circ\)

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