2024 ACS(BR) P1 Q4

2024 ACS(BR) P1 Q4

Secondary 4
6 marks

The diagonals of a cyclic quadrilateral \(PQRS\) intersect at \(U\). The tangent to the circle at \(R\) meets \(PS\) produced at \(T\). If \(QR=RS\), prove that

  1. \(QS\) is parallel to \(RT\),[3]
  2. triangles \(QUR\) and \(RST\) are similar.[3]

Solution:

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Answer:(a) \(QS\parallel RT\). (b) \(\triangle QUR\sim\triangle RST\) (AA).

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