Which of the following statements about a diameter is incorrect?

The correct answer highlights a fundamental property of diameters in a circle. A diameter is defined as a chord that passes through the center of the circle, making it the longest possible chord. Since a diameter spans the entirety of the circle, it cannot be shorter than any other chord or secant.

A secant line, on the other hand, can intersect the circle at two points, and while it can vary in length, the diameter will always measure the full distance across the circle through its center, ensuring it is the longest segment available within that circle. Therefore, the notion that a diameter can be shorter than a secant contradicts the basic definition and properties of these geometric figures, reaffirming why this is an incorrect statement.

The other statements are indeed correct: a diameter is a special type of chord, it connects two points on the circle specifically including the endpoints of the diameter, and it always runs through the center of the circle.