Multiple choice

To draw a pair of tangents to a circle which are inclined to each other at an angle of $75^{\circ}$. It is required to draw tangents at the endpoints of those two radii of the circle, the angle between them should be.

  1. $105^{\circ}$
  2. $65^{\circ}$
  3. $95^{\circ}$
  4. $75^{\circ}$
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A Correct answer
Explanation

The angle between the tangents and the angle between the radii are supplementary. If the tangents are at 75 degrees, the angle between the radii is 180 - 75 = 105 degrees.

AI explanation

If the angle between the tangents is 75 degrees, the quadrilateral formed by the two radii and the point of intersection has angles of 90, 90, and 75 degrees. The sum of angles in a quadrilateral is 360 degrees, so the angle between the radii equals 360 minus 90 minus 90 minus 75 degrees. This calculation gives the required angle between the radii as 105 degrees.

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