Question

line segment ba is tangent to the circle.
what is the length of line segment ba? round to the nearest unit.
18 units
65 units
88 units
98 units

Explanation:

Step1: Recall tangent-secant theorem

If a tangent $BA$ and a secant $BCD$ are drawn from an external point $B$ to a circle, then $BA^2 = BC \times BD$.

Step2: Calculate length of BD

First, find $BD = BC + CD = 55 + 120 = 175$

Step3: Substitute values into formula

Substitute $BC=55$, $BD=175$ into the theorem:
$x^2 = 55 \times 175$
$x^2 = 9625$

Step4: Solve for x

Take the square root of both sides:
$x = \sqrt{9625} \approx 98.11$
Round to the nearest unit: $x \approx 98$

Answer:

98 units