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.

# 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.
We know that tangent is perpendicular to radius.
Therefore,  and
By angle sum property,

Substitute the values into the expression.
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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