Question: Given that $\overleftrightarrow{BC}$ is tangent to circle $A$, $AB = 7$, $BC = 24$, find $AC$.
1. **Problem Statement:** We are given a circle with center $A$, a tangent line $\overleftrightarrow{BC}$ touching the circle at point $B$, with $AB = 7$ and $BC = 24$. We need to find the length $AC$.
2. **Key Concept:** The radius drawn to the point of tangency is perpendicular to the tangent line. Therefore, triangle $ABC$ is a right triangle with right angle at $B$.
3. **Formula Used:** By the Pythagorean theorem for right triangle $ABC$:
$$AC^2 = AB^2 + BC^2$$
4. **Substitute Known Values:**
$$AC^2 = 7^2 + 24^2$$
$$AC^2 = 49 + 576$$
$$AC^2 = 625$$
5. **Calculate $AC$:**
$$AC = \sqrt{625} = 25$$
6. **Answer:** The length $AC$ is $25$.