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.

kite

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rhombus

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square

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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 $O R = P R$ .

Hence, OQPR may or may not be a rhombus.

Thus, OQPR is a kite necessarily.

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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.

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