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      Question

      AB is the diameter of a circle with centre 'O'. PQ is a

      chord that cuts AB at 'C'. If radius of the circle is 7.5 cm and AC:CB = 3:2, the find the length of PQ, given that PC ⊥ AB.
      A 6√6 cm Correct Answer Incorrect Answer
      B 2√3 cm Correct Answer Incorrect Answer
      C √6 cm Correct Answer Incorrect Answer
      D None of these Correct Answer Incorrect Answer

      Solution

      Image
      Since, AB ⊥ PQ, PC = CQ

      Let PC = 'x' cm

      So, AC = 7.5 X 2 X (3/5) = 9 cm

      And, CB = 15 - 9 = 6 cm

      Therefore, AC X CB = PC X PQ

      So, 9 X 6 = x X x

      Or, x 2  = 54

      So, x = 3√6 {Since, length cannot be negative}

      So, PQ = 2x = 6√6 cm

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