Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of 55°it is required to draw tangents at the end points of these two radii of the circle, the angle between two radii is​

Answer 1

Answer:

360-(90°+90°+55°)=125° (by angle sum property of a quadrilateral)

Explanation:

ABO=ACO=90°

bcz angle from centre to the tangent is always 90°

hope it'll help

Answer 2

Question: To draw a pair of tangents to a circle which are inclined to each other at an angle of $60$°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

a. $135$°

b. $90$°

c. $60$°

d. $120$°

Answer:

d.$120$°

Reason:

It is given that

A pair of tangents PQ and PR from the point P touch the circle at Q and R, making O the center of the circle.

∠RPQ = $60$°

We know that

∠OQP = $90$° = ∠ORP

The angle between a tangent to a circle and the radius of the same circle passing through the point of contact is $90$°

Using the angle sum property of quadrilaterals

∠OQP + ∠RPQ + ∠ORP + ∠ROQ = $360$°

Substituting the values

$90$° + $60$° + $90$° + ∠ROQ = $360$°

∠ROQ = $120$°

Therefore, the angle between them should be $120$°.

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