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      Question

      Two chords of a circle 'PQ' and 'RS' crosses each other

      at an exterior point 'O'. Determine the length of the chord 'RS' if the chord PQ is 36 cm long, the chords 'QO' and 'SO' are 12 cm and 8 cm long, respectively. 
      A 64 cm Correct Answer Incorrect Answer
      B 54 cm Correct Answer Incorrect Answer
      C 48 cm Correct Answer Incorrect Answer
      D 28 cm Correct Answer Incorrect Answer

      Solution

      ATQ, QO = 12 cm, SO = 8 cm, and PQ = 36 cm From the secant theorem: PO Ă— QO = RO Ă— SO .... (I) PO = PQ + QO = 36 + 12 = 48 cm Put the value of PO in equation (I) , we get, 48 Ă— 12 = RO Ă— 8 Or, RO = 48 Ă— 12 Ă— (1/8) So, RO = 72 cm Therefore, the length of the chord RS = RO - SO = 72 - 8 = 64 cm

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