MathematicsState whether following statement is true or false.Two tangents P Q and P R are drawn from an external point to a circle with centre O then  QORP is a cyclic quadrilateral.

State whether following statement is true or false.


Two tangents P Q and P R are drawn from an external point to a circle with centre O then  QORP is a cyclic quadrilateral.


  1. A
        True
  2. B
        False 

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    Solution:

    Given are two tangents PQ and PR drawn from external point to a circle with centre O.
     Two tangents PQ and PR are drawn from an external point to a circle with  centre O. Prove that QORP is a cyclic quadrilateralWe know that tangent is perpendicular to radius.
    Therefore, ORP= 90 °  and OQP= 90 °  
    In quadrilateral QORP,
    By angle sum property,
    ORP+RPQ+PQO+QOR= 360 °  
    Substitute the values into the expression. ORP+RPQ+PQO+QOR = 360 ° 90 ° +RPQ+ 90 ° +QOR = 360 ° RPQ+QOR = 360 ° 180 ° RPQ+QOR = 180 °  
    For cyclic quadrilateral, the sum of opposite angles are supplementary.
    Hence, the QORP is a cyclic quadrilateral.
    Therefore the given statement is true.
    Hence option 1 is correct.
     
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