2025 PHS PRELIMS P1 Q8

2025 PHS PRELIMS P1 Q8

Secondary 4
7 marks
2025 Presbyterian High School Prelims A Math Paper 1

In the diagram below, \(TAX\) and \(TCY\) are tangents to the circle at \(A\) and \(C\) respectively. \(AC\) meets \(TD\) at \(E\) and \(D\) is on \(BC\) such that \(TD\) is parallel to \(AB\).

  1. Prove that angle \(ACB\) is equal to angle \(ATD\).[2]
  2. Using the result from part (a), explain whether a circle can be drawn passing through the points \(T\), \(A\), \(D\) and \(C\).[2]

  3. Prove that \(CE \times EA = DE \times TE\).

    [3]

Solution:

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Answer:(a) \(\angle ACB=\angle ATD\). (b) Yes, \(T,A,D,C\) are concyclic. (c) \(CE\times EA=DE\times TE\).

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