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Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements about ∠XYZ are true? (A) Only one (B) Only two (C) Only three (D) All

Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements are true?

(i) It is not possible that \(\angle XYZ\) is an acute angle.

(ii) \(\angle XYZ\) can't be a right angle.

(iii) \(\angle XYZ\) is an obtuse angle.

(iv) Can't make a definite statement for measure of \(\angle XYZ\).

(A) Only one (B) Only two (C) Only three (D) All

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Answer: (C) Only three

For a point on the circle, the angle subtended by the diameter XZ is \(90^\circ\). For a point Y in the interior of the circle (not on XZ), \(\angle XYZ\) is greater than \(90^\circ\), i.e. obtuse.

  • (i) True: it cannot be acute.
  • (ii) True: it cannot be a right angle (that happens only on the circle).
  • (iii) True: it is obtuse.
  • (iv) False: a definite statement (obtuse) can be made.

So three statements are true.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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