2025 SJI PRELIMS P1 Q16

2025 SJI PRELIMS P1 Q16

Secondary 4
4 marks

\(A\), \(B\) and \(C\) lie on a circle. \(AB\) is a diameter, \(AD\) is tangent at \(A\), and \(B,C,D\) are collinear.

  1. Show that triangles \(ABD\) and \(CAD\) are similar.[2]
  2. Given \(BD=25\text{ cm}\), \(DC=9\text{ cm}\), and \(DA=x\text{ cm}\), find \(x\).[2]

Solution:

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Answer:(a) similar (AA) (b) \(15\text{ cm}\)

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