Which of the following statements about $\mathrm{secants}$ and $\mathrm{chords}$ in a $\mathrm{right}\mathrm{triangle}$ is true?

• A. A $\mathrm{secant}$ is a line that intersects a $\mathrm{circle}$ at two points, while a $\mathrm{chord}$ is a segment whose endpoints lie on the $\mathrm{circle}$.
• B. A $\mathrm{secant}$ is always shorter than any $\mathrm{chord}$ in a $\mathrm{right}\mathrm{triangle}$.
• C. $\mathrm{Secants}$ and $\mathrm{chords}$ are the same and can be used interchangeably in $\mathrm{trigonometry}$.
• D. A $\mathrm{chord}$ is a line that touches a $\mathrm{circle}$ at exactly one point.

Answer: (A)

Verified step by step guidance

1. Understand the definitions: A secant is a line that intersects a circle at exactly two points, extending infinitely in both directions, while a chord is a line segment with both endpoints on the circle.
2. Recall that a chord lies entirely inside the circle, connecting two points on the circumference, whereas a secant passes through the circle, intersecting it at two points and continuing beyond the circle.
3. Recognize that a tangent is a line that touches the circle at exactly one point, which is different from both secants and chords.
4. Apply these definitions to the context of a right triangle inscribed in a circle (often the circle is the circumcircle of the triangle), noting that the terms secant and chord refer to lines and segments related to the circle, not specifically to the triangle's sides.
5. Conclude that the correct statement is the one that accurately distinguishes a secant as a line intersecting the circle at two points and a chord as a segment with endpoints on the circle.