S

Question

R
T
M
U
Q
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 168 units long.
Segment upper S upper U is 168 units long.

Segment SU
is 38 units long.
Segment upper S upper U is 38 units long.

Segment SU
is 13 units long.
Segment upper S upper U is 13 units long.

Segment SU
is 42 units long.

Answer 1

To find the length of segment \( SU \), we can use the Secant-Tangent Theorem, which states that if two secant segments \( SQ \) and \( SU \) intersect outside the circle at point \( S \), then:

\[ (SQ) \times (SR) = (SU) \times (ST) \]

From the information provided:

• \( SQ = 21 \)
• \( SR = 8 \)
• \( ST = 4 \)
• \( SU = x \) (unknown length we want to find)

Now we can set up the equation:

\[ 21 \times 8 = x \times 4 \]

Calculating \( 21 \times 8 \):

\[ 168 = 4x \]

Now, divide both sides by 4 to solve for \( x \):

\[ x = \frac{168}{4} = 42 \]

Thus, the length of segment \( SU \) is:

Segment SU is 42 units long.