2026 NCHS P1 Q24

2026 NCHS P1 Q24

Secondary 4
6 marks

\(P\), \(Q\) and \(R\) are points on the circumference of a circle with centre \(O\).

The radius of the circle is 5 m, angle \(QPR=38^\circ\) and angle \(ORP=22^\circ\).

  1. Find angle \(OQP\).
    Give a reason for each step of your working.[3]
  2. Explain if it is possible to draw a circle passing through points \(O\), \(Q\) and \(R\), with \(QR\) as the diameter.[1]
  3. Calculate the area of the shaded segment.[2]

Solution:

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Answer:(a) \(60^\circ\) (b) No: \(\angle QOR=76^\circ\ne90^\circ\). (c) \(4.45\text{ m}^2\).

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