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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Similar questions

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.

Q. PQ and PR are two tangents drawn from an external point P to a circle with centre O. Prove that QORP is a cyclic quadrilateral

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. Points O and P are joined. The ratio of $∠ O P R a n d ∠ O P Q$ is ______.

P A

and

P B

are tangents to the circle with centre

O

from an external point

P

, touching the circle at

A

and

B

respectively. Show that the quadrilateral

A O B P

is cyclic.

State True or False.

PA and PB are tangents to the circle with centre O from an external point P, touching the circle at A and B respectively. Then the quadrilateral AOBP is cyclic.

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