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In the same external-point configuration, the line OP joining the centre O to the external point P:
ALies entirely outside the circle and the chord
BPasses through the midpoint of arc AB only
CIs parallel to the chord AB
DBisects the chord AB at right angles
Answer & Solution
Correct answer: D. Bisects the chord AB at right angles
1. The tangent lengths PA and PB are equal as just shown.
2. The radii OA and OB are also equal.
3. Triangles OAP and OBP are congruent, so OP is a line of symmetry for the figure.
4. By symmetry OP bisects the angle APB and the angle AOB.
5. OP also bisects the chord AB at right angles because it is the perpendicular bisector of AB.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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