Question

*If the measure of angle between two radii of a circle is 60 then the measure of angle between tangents at the outer end of radii is …………*

1️⃣ 30°
2️⃣ 90°
3️⃣ 120°
4️⃣ 60°​

Answer 1

Given : measure of angle between two radii of a circle is 60°

To Find :  the measure of angle between tangents at the outer end  

is

1️⃣ 30°

2️⃣ 90°

3️⃣ 120°

4️⃣ 60°​

Solution:

3️⃣ 120°  is the correct answer.

Two tangents and 2  radius will form a Quadrilateral

angle between radius and tangent  = 90°   each

angle between radii = 60°

angle between tangent   = ?

Su of angles of Quadrilateral = 360°

=> 90°  + 60°  + 90° + angle between tangent   =  360°

=>240° + angle between tangent   =  360°

=> angle between tangent   = 120°

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Answer 2

Given :- If the measure of angle between two radii of a circle is 60 then the measure of angle between tangents at the outer end of radii is …………?

1) 30°

2) 90°

3) 120°

4) 60°

Solution :-

given that,

→ ∠AOB = 60° .

→ 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° .

→ 60° + 90° + 90° + ∠ACB = 360°

→ 240° + ∠ACB = 360°

→ ∠ACB = 360° - 240°

→ ∠ACB = 120° (Option 3) (Ans.)

Hence, the measure of angle between tangents at the outer end of radii is 120° .

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