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.

Answer 1

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.