2026 GESS P2 Q7

2026 GESS P2 Q7

Secondary 4
6 marks

In the diagram, \(AE\) is a tangent to the circle at \(A\). \(ADF\) and \(BCF\) are straight lines, \(AE\) is parallel to \(BF\) and \(AB=CF\).

  1. Prove that \(\angle BAD=\angle DCF\).[1]
  2. Prove that triangle \(ADB\) is congruent to triangle \(CDF\).[3]
  3. Prove that \(\angle ABC=2\angle EAD\).[2]

Solution:

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Answer:(a) Cyclic quadrilateral and straight-line angles. (b) ASA. (c) Congruence gives \(DB=DF\), hence the required double angle.

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