Question
In circle M , secant line SQ and secant line SU intersect at point S outside the circle. If segment SQ=21 , segment SR=8 , and segment ST=4 , find the length of segment SU . (1 point) Responses Segment SU is 38 units long. Segment upper S upper U is 38 units long. Segment SU is 168 units long. Segment upper S upper U is 168 units long. Segment SU is 42 units long. Segment upper S upper U is 42 units long. Segment SU is 13 units long. Segment upper S upper U is 13 units long.
Answers
GPT-4o mini
To find the length of segment \( SU \), we can use the Power of a Point theorem, which states:
\[
(SQ)(SR) = (SU)(ST)
\]
From the problem, we know:
- \( SQ = 21 \)
- \( SR = 8 \)
- \( ST = 4 \)
Let's denote the length of segment \( SU \) as \( x \).
Now we can substitute the known values into the Power of a Point equation:
\[
(21)(8) = (x)(4)
\]
Calculating the left side:
\[
21 \times 8 = 168
\]
Now we have:
\[
168 = 4x
\]
To solve for \( x \), divide both sides by 4:
\[
x = \frac{168}{4} = 42
\]
Thus, the length of segment \( SU \) is \( 42 \) units.
Therefore, the correct response is: **Segment SU is 42 units long.**
\[
(SQ)(SR) = (SU)(ST)
\]
From the problem, we know:
- \( SQ = 21 \)
- \( SR = 8 \)
- \( ST = 4 \)
Let's denote the length of segment \( SU \) as \( x \).
Now we can substitute the known values into the Power of a Point equation:
\[
(21)(8) = (x)(4)
\]
Calculating the left side:
\[
21 \times 8 = 168
\]
Now we have:
\[
168 = 4x
\]
To solve for \( x \), divide both sides by 4:
\[
x = \frac{168}{4} = 42
\]
Thus, the length of segment \( SU \) is \( 42 \) units.
Therefore, the correct response is: **Segment SU is 42 units long.**