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

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