Question
TU
is tangent to ⨀S. What is SU?
S
T
U
15 ft
8 ft
SU=
ft
is tangent to ⨀S. What is SU?
S
T
U
15 ft
8 ft
SU=
ft
Answers
GPT-4o mini
To find the length of SU, we need to use the properties of tangents and circles. When a tangent line touches a circle, it forms a right angle with the radius that meets the point of tangency.
Given the information:
- The length of tangent segment TU = 15 ft
- The length of radius segment SU = 8 ft
Using the right triangle formed by SU, TU, and ST:
1. SU = radius = 8 ft
2. TU = tangent = 15 ft
We can now apply the Pythagorean theorem because \( S \), \( U \), and \( T \) form a right triangle at \( U \):
\[
ST^2 = SU^2 + TU^2
\]
Calculating:
\[
ST^2 = 8^2 + 15^2
\]
\[
ST^2 = 64 + 225
\]
\[
ST^2 = 289
\]
\[
ST = \sqrt{289} = 17 \text{ ft}
\]
Now, to find SU, we already have the radius given \( SU = 8 \text{ ft} \).
So, the answer is:
**SU = 8 ft.**
Given the information:
- The length of tangent segment TU = 15 ft
- The length of radius segment SU = 8 ft
Using the right triangle formed by SU, TU, and ST:
1. SU = radius = 8 ft
2. TU = tangent = 15 ft
We can now apply the Pythagorean theorem because \( S \), \( U \), and \( T \) form a right triangle at \( U \):
\[
ST^2 = SU^2 + TU^2
\]
Calculating:
\[
ST^2 = 8^2 + 15^2
\]
\[
ST^2 = 64 + 225
\]
\[
ST^2 = 289
\]
\[
ST = \sqrt{289} = 17 \text{ ft}
\]
Now, to find SU, we already have the radius given \( SU = 8 \text{ ft} \).
So, the answer is:
**SU = 8 ft.**