The angle subtended by a chord at the center is 120°. The angle between the chord and the tangent at one endpoint is:
Show answer & explanation
Correct answer: B
Explanation
Let the chord be AB and the tangent touch the circle at A.
Angle AOB = 120°
Since OA = OB (radii), triangle OAB is isosceles.
∠OAB = ∠OBA
∠OAB = (180° − 120°) / 2
= 60° / 2
= 30°
Also, radius OA is perpendicular to the tangent at A.
Therefore,
Angle between chord and tangent
= 90° − 30°
= 60°
Answer: 60°