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To draw a pair of tangents to a circle which are inclined to each other at an angle of $60^{o}$ , it is required to draw tangents at endpoints of those two radii of the circle, the angle between them should be:

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135^{0}

90^{0}

60^{0}

120^{0}

answer is D.

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Detailed Solution

Given that a pair of tangents are inclined to each other at an angle of

60^{o}

.
Let, O be the center of a circle to which a pair of tangents PQ & PR from a
point P touches the circle at Q&R respectively,

∠ RPQ

= 60°.
Drawing the required figure,
Question Image

∠

OOP=90°=

∠

ORP as the angle, between a tangent to a circle and the radius of the same circle passing through the point of contact, is 90°.
In quadrilateral PQOR,
By angle sum property of quadrilaterals,

∠

OQP+

∠

RPQ +

∠

ORP +

∠

ROQ=360°

\Rightarrow

90°+ 60°+90°+

∠

ROQ =360°

\Rightarrow ∠

ROQ =360°-240°

\Rightarrow ∠

ROQ =120°.
Thus, the required angle is 120°.
Therefore, option (4) is correct.

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