The angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the circle. Therefore, the required angle is 35°.
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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.
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.
Using the chord-length formula or the Baudhāyana–Pythagoras Theorem, the half-chord measures √13 cm. Therefore, the complete chord length is 2√13 cm.
Using the Baudhāyana–Pythagoras Theorem, equal chords with equal radii give equal perpendicular distances from the centre. Hence, chords of equal length are always equidistant from the centre of the circle.