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Given: Radius of small circle (centre P), PA = PB = 5 cm.

Mathematics

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  1. a)
  1. Draw a diagram.

    Let M be the midpoint of the common chord AB. The line connecting the centers P and Q passes through M and is perpendicular to AB.
    Given: Radius of small circle (centre P), PA=PB=5 cmPA = PB = 5 \text{ cm}.
    Radius of big circle (centre Q), QA=QB=6 cmQA = QB = 6 \text{ cm}.
    Length of common chord AB=8 cmAB = 8 \text{ cm}.
    Since M is the midpoint of AB, AM=MB=12×8=4 cmAM = MB = \frac{1}{2} \times 8 = 4 \text{ cm}.

  2. Calculate the length of PM using the Pythagorean theorem in $\triangle PMA

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