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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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.
Equal perpendicular distances from the centre imply that the two chords are equidistant from the centre. By Theorem 7, chords equidistant from the centre of a circle are equal. Therefore, AB = GF.