Question

If angle between two radii of a circle is 125°, then the angle between tangents at the ends of radii​

Answer 1

Angle at the ends of the tanget and the angle between radii is saplementory

therefore angle at radii + angle at enda of tanget =180

angle at end of the tanget = 180-125

=55 degree

Ans angle at the end of the tangets will be 55 degree

Answer 2

Given :- If the measure of angle between two radii of a circle is 125°, then the measure of angle between tangents at the outer end of radii is …………?

Solution :-

given that,

→ ∠AOB = 125° .

→ 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° .

→ 125° + 90° + 90° + ∠ACB = 360°

→ 305° + ∠ACB = 360°

→ ∠ACB = 360° - 305°

→ ∠ACB = 55° (Ans.)

Hence, the measure of angle between tangents at the outer end of radii is 55° .

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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