The perpendicular from the centre to the chord bisects it. Half the chord is 8 cm. Using the right triangle, radius² = 8² + 6² = 100. Therefore, radius = 10 cm.
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In a cyclic quadrilateral, opposite angles are supplementary. Therefore, ∠C = 180° – 75° = 105°. Similarly, ∠D = 180° – 110° = 70°.
The perpendicular from the centre to the chord bisects the chord. With radius 15 cm and distance 9 cm, half the chord is 12 cm. Therefore, the chord length is 24 cm.
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.
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.