Question

line segment qp is tangent to the circle.
what is the length of line segment qp? round to the nearest unit.
13 units
17 units
18 units
20 units
the circle has a diameter mn of length 24, and the length of np is 11.5, qp is labeled as n.

Explanation:

Step1: Identify tangent-secant formula

For a tangent segment $QP$ and a secant segment $PM$ with external segment $PN$, the formula is $QP^2 = PN \times PM$.

Step2: Calculate length of PM

The diameter $MN=24$, so the radius is 12, and $PM = MN + NP = 24 + 11.5 = 35.5$.

Step3: Substitute values into formula

$QP^2 = 11.5 \times 35.5$
$QP^2 = 408.25$

Step4: Solve for QP

$QP = \sqrt{408.25} \approx 20.205$

Step5: Round to nearest unit

Round $20.205$ to the nearest whole number.

Answer:

20 units