2025 CGS PRELIMS P1 Q12

2025 CGS PRELIMS P1 Q12

Secondary 4
8 marks
2025 Crescent Girls' School Prelims A Math Paper 1

The diagram shows two circles intersecting at \(D\) and \(F\).

\(ABC\) is a tangent to the bigger circle at \(B\) and \(BFH\) is a tangent to the smaller circle at \(F\).

\(ADF\), \(BDE\) and \(GFE\) are straight lines.

It is given that angle \(BFG=x^\circ\).

  1. Prove that triangle \(BGF\) is an isosceles triangle.[4]
  2. Show that \(CBA\) is parallel to \(GFE\).[2]
  3. Show that triangle \(ABD\) is similar to triangle \(BEG\).[2]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) \(BF=BG\), so \(\triangle BGF\) is isosceles. (b) \(CBA\parallel GFE\). (c) \(\triangle ABD\sim\triangle BEG\).

Need help? Join our JC Math tuition classes.

Learn more