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IP2U13 13.4 PN1 Q12

IP2U13 13.4 PN1 Q12

IP 2

The diagram shows two circles, with centres \(A\) and \(B\), each of radius \(5\) cm, touching each other externally at \(X\). Both of them touch another bigger circle, with centre \(O\) and radius \(13\) cm, internally at \(D\) and \(C\) respectively.

  1. Show that \(\angle COD\) is \(1.35\) radians.
  2. Calculate
    1. the perimeter and
    2. the area of the shaded region.

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Answer:(a) \(1.35\) rad (b)(i) \(40.0\) cm (b)(ii) \(26.7\text{ cm}^2\)

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