Question

to draw a pair of tangent to a circle which are included to each other at an angle of 60 it is required to draw tangent at end of point of those two radii of circle what should be the angle between them
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Answer 1

Step-by-step explanation:

Thus, QP and PR are the required tangents inclined to each other at an angle of 60°. Hence, QP and PR are tangents inclined to each other at an angle of 60°.

Answer 2

Answer:

Question ::

Construct a pair of tangents to a circle which are inclined to each other at an angle of 60 degree.

SOLUTION :::

We know that radius of the circle is perpendicular to the tangents.

Sum of all the 4 angles of quadrilateral = 360°

∴ Angle between the radius (∠O) = 360° - (90° + 90° + 60°) = 120°

✍Steps of Construction:✒

Step I: A point Q is taken on the circumference of the circle and OQ is joined. OQ is radius of the circle.

Step II: Draw another radius OR making an angle equal to 120° with the previous one.

Step III: A point P is taken outside the circle. QP and PR are joined which is perpendicular OQ and OR.

Thus, QP and PR are the required tangents inclined to each other at an angle of 60°.

✍Justification:✒

Sum of all angles in the quadrilateral PQOR = 360°

∠QOR + ∠ORP + ∠OQR + ∠RPQ = 360°

⇒ 120° + 90° + 90° + ∠RPQ = 360°

⇒∠RPQ = 360° - 300°

⇒∠RPQ = 60°

Hence, QP and PR are tangents inclined to each other at an angle of 60°.

Step-by-step explanation:

$Hope \: it \: helps...!!$