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Circles — Maths STD 9 — Question

CBSE BoardEnglish MediumSTD 9MathsCircles1 Mark
MCQ
Statement-1 (A): If A, B, C, D are four points such that $\angle B A C=30^{\circ}$ and $\angle B D C=60^{\circ}$, then D is the centre of the circle through A, B and C.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • ✓
    Statement-1 is False, Statement-2 is True.
✓

Answer

Correct option: D.
Statement-1 is False, Statement-2 is True.
(d)
Statement-2 is true.
Statement-1 is not true, because there can be many points D such that $\angle B D C=60^{\circ}$ and each such point cannot be the centre of the circle through A, B, C. Hence, option (d) is correct.

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