The angle between two radii of a circle is 105°, the angle between the tangents at the ends of the radii is: The angle between two radii of a circle is 105°, the angle between the tangents at the ends of the radii is:
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not a prblm divya i am good in maths i will solve it♥️♥️
angle between tangents is 180-105=75°
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Given :- If the measure of angle between two radii of a circle is 105°, then the measure of angle between tangents at the outer end of radii is …………?
Solution :-
given that,
→ ∠AOB = 105° .
→ 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° .
→ 105° + 90° + 90° + ∠ACB = 360°
→ 285° + ∠ACB = 360°
→ ∠ACB = 360° - 285°
→ ∠ACB = 75° (Ans.)
Hence, the measure of angle between tangents at the outer end of radii is 75° .
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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