Yes. If X and Y lie on the same side of AB on the circle, then ∠AXB and ∠AYB subtend the same chord AB. Hence, they are equal, so they cannot be different.
Let A and B be two points on a circle with centre O. (i) Are there points X, Y on the circle, on the same side of AB, such that ∠AXB is different from ∠AYB?
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No. There cannot be such points X and Y on the same side of AB for which ∠AXB is different from ∠AYB. According to Theorem 9, an arc subtends the same angle at every point on the remaining part of the circle. Therefore, when X and Y lie on the same side of AB, both angles subtend the same chord AB and are equal.
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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