Yes. If ∠AXB = ∠AYB, then A, B, X and Y are concyclic, provided X and Y are on the same side of AB. This follows from Theorem 10.
If ∠AXB = ∠AYB and X and Y do not lie on the circle, does the circle through A, B and X also pass through Y?
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Yes. If ∠AXB = ∠AYB, then A, B, X and Y are concyclic, provided X and Y are on the same side of AB. This follows from Theorem 10.
Yes. Since ∠AXB = ∠AYB, the line segment AB subtends equal angles at X and Y. If X and Y are on the same side of AB, Theorem 10 states that the four points A, B, X and Y lie on a circle. Therefore, the circle passing through A, B and X will also pass through Y. Thus, A, B, X and Y are concyclic.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
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