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Applications of Circle Symmetric Property 4

Applications of Circle Symmetric Property 4

TGM Original

The diagram shows a circle, centre \(O\) and radius \(3\) cm.
If \(CA\) and \(CB\) are tangents to the circle at \(A\) and \(B\) respectively and \(AC=8\) cm, find

  1. the length of \(BC\),
  2. the length of \(OC\),
  3. the area of the quadrilateral \(AOBC\).

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Answer:(a) \(8\text{ cm}\) (b) \(\sqrt{73}\text{ cm}\approx8.54\text{ cm}\) (3 s.f.) (c) \(24\text{ cm}^2\)

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