Two tangents drawn from a point P outside the circle touch the circle at M and N- Then MONP is aA- ParallelogramB- RectangleC- Cyclic quadrialteral

The correct option is C Cyclic quadrialteral ∠ PNO = ∠ PMO =90^∘ ( ∵ tangent and radius at the point of contact are perpendicular to each other.) Therefore∠ MO ...

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Standard X

Mathematics

Construction of Tangent When Point is on the Circle

Two tangents ...

Question

Two tangents drawn from a point P outside the circle touch the circle at M and N. Then MONP is a

Parallelogram

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Rectangle

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Cyclic quadrialteral

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Solution

The correct option is C Cyclic quadrialteral

$∠ P N O = ∠ P M O = 90^{\circ}$ ( $∵$ tangent and radius at the point of contact are perpendicular to each other.)

Therefore $∠ M O N + ∠ M P N = 180^{\circ}$
( $∵$ sum of angles in a quadrilateral is $360^{\circ}$ )

Thus MONP is a cyclic quadrilateral.

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Two tangents drawn from a point P outside the circle touch the circle at M and N. Then MONP is a

The correct option is C Cyclic quadrialteral ∠PNO=∠PMO=90∘ ( ∵ tangent and radius at the point of contact are perpendicular to each other.) Therefore∠MON+∠MPN=180∘ (∵ sum of angles in a quadrilateral is 360∘) Thus MONP is a cyclic quadrilateral.