A chord is the straight line BX (in the figure). We know that the length of the maxium chord we can construct is closest to the diameter of the circle. In an extreme case, lets suppose that the length of the chord is the diameter of the circle . In that case, we have:

\(diameter = 15\)
therefore,
\(r = 7.5\)
In conclusion, the length of the circumference is given by:
\(C = 2\pi r\)
\(C = 15\pi\)

In this case, A > B, option A.

Now, lets suppose that the chord is less than the diameter. In this situation, we are completely sure that the diameter is more than 15, therefore, the length of the circumference is more than \(15\pi\). In conclusion, A > B, Option A.

1) All diameters are chords but not all chords are diameters
2) The diameter is the longest line in the circle

Using these two rules, we can conclude that the diameter of our circle is equal to or greater than 15, and its circumference is thus equal to or greater than 15*pi. Therefore Quantity A will always be greater.

The diameter is the largest chord.
if chord= 15, diameter is 15 or more than 15.
so, circumference is 15 pi or more than 15pi.

So, Q A is greater.

Piece of cake.
If the chord AB is the diameter of the circunsference, its perimeter is 15π which is larger than 12π.
If the chord AB isn´t the diameter of the circunsference, its perimeter is larger than 15π which is larger than 12π.

Answer A

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