Maths

PQ and PR are tangents to the circle centred at O. If OPR = 45°, then prove that ORPQ is a square.

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  1. OPR is 1/2 QPR
    The tangents are perpendicular to the radii.

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  2. Ang OPR = 1/2 Ang RPQ
    Hence, Ang RPQ = 90°
    Ang QOR = 90° ( Supplementary angles in a cyclic quadrilateral )

    Also, Ang OQP = Ang ORP = 90° ( radii perpendicular to tangents)

    Hence, we can say ORPQ is a square.

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