Question

# Two tangents are drawn from an external point P that touches the circle at points Q and R respectively. The centre of the circle is O. The lines OQ and OR are drawn to complete the quadrilateral OQPR. The resulting quadrilateral is a ________necessarily.

A

kite

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B

rhombus

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C

square

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D

rectangle

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Solution

## The correct option is A kite PQ = PR (Tangents drawn from an external point to the circle are equal in length.) OQ = OR (Radius of the circle.) Thus, when the pairs of adjacent sides through the opposite vertices are equal, the quadrilateral is a “kite”. Also, it is not given that OR=PR. Hence, OQPR may or may not be a rhombus. Thus, OQPR is a kite necessarily.

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