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Standard X

Mathematics

Lengths of Tangents Drawn from External Point

In the figure...

Question

In the figure, KLMN is a cyclic quadrilateral and PQ is a tangent to the circle at K. If LN is a diameter of the circle. $∠ K L N = 30^{\circ}$ and $∠ M N L = 60^{\circ}$ . Determine $∠ Q K N$

30^{\circ}

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60^{\circ}

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90^{\circ}

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100^{\circ}

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Solution

The correct option is A $30^{\circ}$
$K N$ is a chord through the point of contact $K$ .
$∴ ∠ Q K N = ∠ K L N$
[Angles in the alt. segment are equal] = $30^{\circ}$

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In the figure, KLMN is a cyclic quadrilateral and PQ is a tangent to the circle at K. If LN is a diameter of the circle. ∠KLN=30∘ and ∠MNL=60∘. Determine ∠QKN

The correct option is A 30∘KN is a chord through the point of contact K.∴∠QKN=∠KLN[Angles in the alt. segment are equal] = 30∘

In the figure, KLMN is a cyclic quadrilateral and PQ is a tangent to the circle at K. If LN is a diameter of the circle. $∠ K L N = 30^{\circ}$ and $∠ M N L = 60^{\circ}$ . Determine $∠ Q K N$

The correct option is A $30^{\circ}$
$K N$ is a chord through the point of contact $K$ .
$∴ ∠ Q K N = ∠ K L N$
[Angles in the alt. segment are equal] = $30^{\circ}$