From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. The lines OQ and OR are drawn to complete the quadrilateral OQPR. The resulting quadrilateral is a ___.

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

The tangents are equal in length. Hence, PQ = PR. The radii are equal in length. Hence, OQ = OR. Thus, when the pairs of adjacent sides through opposite vertices are equal, the quadrilateral is called “kite”.

Two pairs of adjacent sides (OR and OQ, PR and PQ) are equal. Hence, the quadrilateral is a kite.

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