https://file.aiquickdraw.com/mathbot/file/17255472217559ghdurig.jpg

Which of the following is true about *AB* in the figure given?


*AB* is a secant to the circle, *C*.

*AB* is a tangent to the circle, *C*.

*AB* is a chord to the circle, *C*.

*AB* is NOT a tangent to the circle, *C*.

From the given image, we can make the following observations:

- \( AB \) is a line that intersects the circle at point \( A \), but not at any other point on the circumference.
- A tangent is a line that touches the circle at exactly one point, and \( AB \) does exactly this at point \( A \).
- The other line from \( B \) to point \( A \) does not intersect the circle at any other point, confirming it touches the circle at just one point.

### Conclusion:
The correct answer is that **\( AB \) is a tangent to the circle, \( C \)**.

Let me know if you would like further clarification, and here are some related questions to expand upon:

1. What is the definition of a secant in relation to circles?
2. How do we prove a line is tangent to a circle geometrically?
3. Could \( AB \) ever be a chord if modified?
4. What is the relationship between the radius \( CA \) and the tangent \( AB \)?
5. How can we use Pythagoras' theorem to analyze this configuration?

**Tip:** For tangent lines, the radius at the point of contact is always perpendicular to the tangent.

Which of the following is true about AB in the figure given?

1. AB is a secant to the circle, C.
2. AB is a tangent to the circle, C.
3. AB is a chord to the circle, C.
4. AB is NOT a tangent to the circle, C.

Learn how to identify whether a line is a tangent, secant, or chord to a circle with this detailed explanation. Using key circle geometry theorems such as the tangent-secant theorem and Pythagoras' theorem, the problem walks through how to determine the nature of the line AB in the given figure. Suitable for students in Grades 8-10.

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