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Tangent-chord (alternate segment) theorem: the angle between a chord and the tangent at one end equals which inscribed angle?
Answer & Solution
Correct answer: D.
1. The tangent-chord angle equals half the central angle of the chord.
2. An inscribed angle on the opposite arc subtends the same chord and equals half the same central angle.
3. Both quantities equal x/2, so they are equal to each other.
4. The inscribed angle on the same arc as the tangent equals (180° − x)/2 and is the supplement of the tangent-chord angle (with the chord).
5. Hence the matching inscribed angle lies on the opposite arc.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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