Multiple choice

Write true or false and give reasons for your answers. If a chord AB subtends an angle of ${60^0}$ at the centre of a circle , then the angle between the tangents at A and B is also ${60 ^0}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The tangents at A and B form a quadrilateral with the center. The angles between the radius and tangent are 90 degrees. If the central angle is 60, the angle between tangents is 180 - 60 = 120 degrees.

AI explanation

The two tangents at A and B and the chord AB form an isosceles triangle where the angle between the tangent and chord at each end equals 60 degrees by the alternate segment theorem. The angle between the two tangents is supplementary to the angle subtended at the center by the chord. Therefore, the angle between the tangents is 180 degrees minus 60 degrees, resulting in 120 degrees, not 60 degrees. The statement is consequently false.

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