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    Question

    O and C are the respectively orthocentre and

    circumcentre of ∆PQR. The line PO is extended which intersect line QR at S. such that, ∠QCR = 140°, ∠PQS = 58°. Find ∠RPS = ?
    A 29° Correct Answer Incorrect Answer
    B 38° Correct Answer Incorrect Answer
    C 41° Correct Answer Incorrect Answer
    D 32° Correct Answer Incorrect Answer

    Solution

    In ∆ PQS  ∠QPS + ∠PQS + ∠PSQ = 180° ∠QPS + 58° + 90° = 180° ∠QPS = 32° ∠QCR = 2∠QPR (∠QCR)/2 = ∠QPR 140/2 = ∠QPS + ∠RPS 70° = 32° + ∠RPS ∠RPS = 38°

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