Question

if angle between two radii of circle is 120°, the angle between the tangents at the ends of radii is......​

Answer 1

Answer:

Radius is perpendicular to the Tangent.

So the quadrilateral formed by the radii and the tangent will be concyclic.

The angle between the tangents =

180 -120 = 60°

Answer 2

Given :- If the measure of angle between two radii of a circle is 120°, then the measure of angle between tangents at the outer end of radii is …………?

Solution :-

given that,

→ ∠AOB = 120° .

→ OA = OB = radius .

we know that,

• Radius is perpendicular to the tangent at the point of contact .
• sum of interior angles of a quadrilateral is 360° .

So,

→ ∠OAC = ∠OBC = 90° .

therefore,

→ ∠AOB + ∠OAC + ∠OBC + ∠ACB = 360° .

→ 120° + 90° + 90° + ∠ACB = 360°

→ 300° + ∠ACB = 360°

→ ∠ACB = 360° - 300°

→ ∠ACB = 60° (Ans.)

Hence, the measure of angle between tangents at the outer end of radii is 60° .

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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