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The angle between a tangent to a circle and a chord drawn from the point of contact is related to the chord's central angle as:
Answer & Solution
Correct answer: C.
1. Let the chord central angle be x degrees, and consider the isosceles triangle formed by the chord and the two radii to its endpoints.
2. The base angles of that isosceles triangle each measure (180° − x)/2 = 90° − x/2.
3. The radius to the contact point is perpendicular to the tangent.
4. So the angle between the tangent and the chord at the contact equals 90° − (90° − x/2) = x/2.
5. Hence the tangent-chord angle is half the central angle of the chord.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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