Question

What is the value of x?

Answer 1

The only way you can answer this is if x meets the chord at right angles or if x bisects the chord at the chord's midpoint. Otherwise the problem is unsolvable. Since neither of the two conditions have been met in the givens of the problem, I would say that you can't do it.

However having expressed that opinion, I think whoever gave you the problem expects you to say that since the two chords are equal and since x looks like it bisects the chord, that x = 16 because congruency can be shown.

Answer 16

but its not the best question I've seen.

Answer 2

The angle between the segment labled x and the chord labeled 30 is not specified. The measure of x cannot be determined, except to say that it is somewhere between 16 and the radius of the circle, √(16²+15²) = √481 ≈ 21.93.

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If the angle between x and the chord were marked as a right angle, one could say x=16, because all chords of the same length are the same distance from the center of the circle.