Multiple choice

if the angle between the radii of a circle is ${130}^{0}$ then the angle between the tangents at the ends of the radii is

  1. ${90}^{0}$
  2. ${70}^{0}$
  3. ${50}^{0}$
  4. ${40}^{0}$
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C Correct answer
Explanation

The angle between the radii and the tangents at their endpoints is 90 degrees. In the quadrilateral formed by the center, the two points of tangency, and the intersection of the tangents, the sum of angles is 360 degrees. The angle between the tangents is 180 - 130 = 50 degrees.

AI explanation

The angle between two tangents drawn from an external point and the angle subtended by their points of tangency at the center of the circle are supplementary. This relationship comes from the fact that the radii and tangents form a quadrilateral with two 90 degree angles. Therefore, the angle between the tangents is 180 degrees minus 130 degrees. The resulting angle between the tangents is 50 degrees.

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