Multiple choice

To construct a pair of tangents to a circle at an angle of 60° to each other, it is needed to draw tangents at endpoints of those two radii of the circle, the angle between them should be:

  1. 1000

  2. 900

  3. 800

  4. 1200
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D Correct answer
Explanation

The tangents to a circle from an external point form a quadrilateral with the two radii. The angles between the radii and the tangents are 90 degrees. If the angle between tangents is 60 degrees, the angle between the radii must be 180 - 60 = 120 degrees.

AI explanation

The radius to a point of tangency is perpendicular to the tangent line, so the two tangents and two radii form a quadrilateral with two right angles. If the angle between the tangents is 60 degrees, the remaining angle between the radii must be 360 - 90 - 90 - 60 = 120 degrees. The needed angle between the radii is 120 degrees.

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