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The diagram depicts a geometric problem involving a circle, with a tangent line, some triangle and segment labels, and known lengths. The goal is to find the radius of the circle.

### Key observations from the diagram:
- There is a right triangle \( \triangle ABC \), where \( AB \) is the radius \( r \), and \( BC \) is perpendicular to the tangent.
- \( AC = 16 \), \( CD = 13 \), and \( DE = 14 \), which seem to correspond to a path along a straight line.
- \( BF \) is tangent to the circle at \( B \), making \( \angle ABC = 90^\circ \), which gives a right triangle \( \triangle ABC \).

We can solve for the radius \( r \) using the Pythagorean theorem, since \( \triangle ABC \) is a right triangle:

\[
AB^2 + BC^2 = AC^2
\]

Where \( AB = r \), \( AC = 16 \), and \( BC = 13 \) (since it appears adjacent to \( CD \)).

Let's calculate \( r \).The radius \( r \) of the circle is approximately \( 9.33 \) units.

Would you like more details or have any questions?

Here are five related questions to expand on this problem:
1. How does the tangent line affect the properties of the triangle \( \triangle ABC \)?
2. Can you calculate the angle at point \( A \) in triangle \( \triangle ABC \)?
3. How would the calculation change if the distance \( BC \) was different?
4. Can you find the length of the segment \( BE \) using other methods?
5. How would the area of the circle be determined from the radius?

**Tip**: In problems involving tangents and circles, the key property is that the tangent is perpendicular to the radius at the point of contact.

Learn how to find the radius of a circle using a right triangle and the Pythagorean Theorem. In this problem, the tangent property and known triangle lengths help solve for the circle's radius. Suitable for Grades 8-10 students.

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