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Tangent-chord (alternate segment) theorem: the angle between a chord and the tangent at one end equals which inscribed angle?
AAny inscribed angle on the same arc as the tangent
BHalf the inscribed angle on the same arc as the tangent
CTwice the inscribed angle on either arc
DThe inscribed angle on the arc on the opposite side of the chord
Answer & Solution
Correct answer: D. The inscribed angle on the arc on the opposite side of the chord
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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