In the figure, radii divide the opposite angles into parts. Using the isosceles triangles formed by equal radii, we get p + v = 90° and q + u = 90°. Hence, opposite angles sum to 180°.
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As written, this statement appears inconsistent with the figure/text. Since each chord is perpendicular to diameter AB, its midpoint lies on AB. Therefore, the segment joining the two midpoints lies along AB, so it is parallel to AB, not perpendicular.
The diameter passes through the centre and is the longest chord of a circle. Any other chord lies away from the centre and is therefore shorter than the diameter. Hence, no chord is longer.
Half of the chords are 5 cm and 12 cm. Let the distance of the 24 cm chord from the centre be x. Then the other is x + 7. Solving gives x = 5 and radius = 13 cm.
In a rectangle, the diagonals are equal and bisect each other. Since the rectangle is cyclic, each diagonal is a diameter of the circle. Therefore, their intersection is the midpoint of a diameter, which is the centre.