Yes, provided X and Y lie on the same side of AB. Angles subtended by the same chord at points on the same segment of a circle are equal.
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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.
Since OA and OB are radii, triangle AOB is isosceles. Given ∠AOB = 60°, the other two angles are also 60°. Thus, triangle AOB is equilateral, so AB = OA = 12 cm.
No, we cannot conclude that CD = 2AB. According to the chapter, the longer chord is closer to the centre. Chord length depends on radius and distance from the centre, not directly on distance alone.
This six-term polynomial matches the three-term square identity. Looking at the negative signs, the bases for both v and w must be negative to yield the correct cross-product signs.