The quadrilateral ABCD is cyclic. The opposite angles of a cyclic quadrilateral are supplementary. So, x + 100° = 180° Therefore, x = 80°.
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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.
The perpendicular from the centre bisects the chord, forming two right triangles. Applying the Baudhāyana–Pythagoras Theorem gives the half-chord as √(r² − d²). Hence, the chord length is 2√(r² − d²).
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.