2026 PHS P1 Q8

2026 PHS P1 Q8

Secondary 4
3 marks

The diagram shows a triangular garden \(PQR\).

A sprinkler is to be installed inside the garden.

  1. Construct the bisector of angle \(RQP\).[1]
  2. Construct the perpendicular bisector of \(QR\).[1]
  3. The sprinkler is to be placed nearer to \(PQ\) than to \(RQ\), and nearer to \(Q\) than to \(R\). Shade the region inside the garden where the sprinkler can be placed.[1]

Solution:

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Answer:(a), (b) See construction. (c) The shaded intersection towards \(PQ\) and \(Q\), excluding both bisectors.

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