If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is
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Answer:
If the angle between the two radii of circle is 110 degrees the angle between the tangent at the ends of these radii is - 8063112. ... two tangents= 360° so, 90°+90°+110°+angle between tangents=360 °
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Given :- If the measure of angle between two radii of a circle is 110°, then the measure of angle between tangents at the outer end of radii is …………?
Solution :-
given that,
→ ∠AOB = 110° .
→ 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° .
→ 110° + 90° + 90° + ∠ACB = 360°
→ 290° + ∠ACB = 360°
→ ∠ACB = 360° - 290°
→ ∠ACB = 70° (Ans.)
Hence, the measure of angle between tangents at the outer end of radii is 70° .
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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