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2026 NYGH P1 Q11

2026 NYGH P1 Q11

IP 4
8 marks

In the diagram, \(A\), \(B\) and \(C\) are points on a circle, centre \(O\) and radius, \(OA=6\text{ cm}\). A smaller circle, centre \(X\), passes through \(B\) and \(O\). The line segment \(AC\) is tangent to the smaller circle at point \(Y\).

  1. Show that angle \(BOC\) is \(0.680\) radian.[2]
  2. Find the total perimeter of both shaded regions.[6]

Solution:

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Answer:(a) \(\angle BOC=2\sin^{-1}\left(\dfrac13\right)=0.680\) radian (3 s.f.) (b) \(30.0\text{ cm}\).

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