A circle has radius 13. A chord of the circle has length 24. What is the distance from the center of the circle to the chord?

The perpendicular from the center of a circle to a chord bisects the chord. So the 24-unit chord is split into two segments of length 12, and the radius 13 to the chord's endpoint forms the hypotenuse of a right triangle with legs $d$ and 12. By the Pythagorean theorem, $d^2 + 12^2 = 13^2$, so $d^2 = 169 - 144 = 25$ and $d = 5$, choice A. This is the 5-12-13 triple. Choice B (11) comes from $13 - 2$ or a subtraction slip. Choice C (12) is half the chord, not the distance. Choice D (7) comes from $\sqrt{49}$ after miscomputing $169 - 120$.