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An equilateral triangle is circumscribed about a circle, meaning each side of the triangle is a tangent to the circle. The angle between the two radii drawn to consecutive points of contact is:
Answer & Solution
Correct answer: A.
1. In an equilateral triangle each interior angle is 60°.
2. Adjacent tangent and radius lines meet at 90° at the contact point.
3. The angle between the tangents (the triangle's vertex angle) and the angle between the corresponding radii are supplementary.
4. So the angle between consecutive radii = 180° − 60° = 120°.
5. Three such radii at 120° apart give the equilateral configuration.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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