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Calculation of Unknown Lengths in Circular Segments

Calculation of Unknown Lengths in Circular Segments

Secondary 3

\(TA\) and \(TB\) are tangents to a circle centre \(O\) and \(AT\) produced meets \(OB\) at \(Y\).
\(YB=12\) cm, \(TB=5\) cm and \(OA=r\) cm.

  1. Write down the length of \(TA\).
  2. Calculate the length of \(TY\).
  3. Without solving (d), find the numerical value of \(\frac{OA}{AY}\).
  4. Calculate the value of \(r\).

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Answer:(a) \(5\text{ cm}\) (b) \(13\text{ cm}\) (c) \(\frac5{12}\) (d) \(7.5\text{ cm}\)

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