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.
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Apply the Baudhāyana–Pythagoras Theorem to the right triangles formed by the radii and perpendiculars. Equal radii and equal perpendicular distances give equal half-chords. Hence, the complete chords are equal.
The perpendicular distances of the two chords from the centre are found using the Pythagoras Theorem. Since the chords lie on opposite sides of the centre, the required distance is the sum of these distances, which is seven centimetres.
The two triangles have equal radii as corresponding sides and equal chord lengths as their bases. Therefore, all three corresponding sides are equal, so the triangles are congruent by the SSS Congruence Criterion.
No. There is no point that is equally distant from three collinear points. The perpendicular bisectors of AB and BC are parallel and never intersect. Therefore, no circle can pass through three collinear points.