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      Question

      A tangent is drawn from an external point P to a circle,

      touching the circle at point Q such that PQ = 16cm. A secant PRS is also drawn from P, intersecting the circle at points R and S. Given that PR = 8 cm, determine the length of the chord RS.
      A 24 cm Correct Answer Incorrect Answer
      B 12 cm Correct Answer Incorrect Answer
      C 16 cm Correct Answer Incorrect Answer
      D 18 cm Correct Answer Incorrect Answer

      Solution

      Image

      We know that,

      PQ 2  = PR × PS (Tangent secant theorem)

      So, 16 2  = 8 × PS

      Or, 256 = 8 × PS

      Or, PS = 32 cm

      RS = PS – PR

      So, RS = 32 – 8 = 24 cm
      Therefore, the length of chord is 24 cm.

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