line segment ba is tangent to the circle. what is the length of line segment ba? round to the nearest unit…

Explanation:

Step1: Apply tangent - secant rule

If a tangent and a secant are drawn to a circle from an exterior point, then the square of the length of the tangent is equal to the product of the lengths of the secant and its external segment. Here, $BA$ is the tangent, $BD$ is the secant, and $BC$ is the external segment of the secant. Let $BA = x$, $BC=55$, and $BD=55 + 120=175$. The formula is $x^{2}=BC\times BD$.

Step2: Substitute values

Substitute $BC = 55$ and $BD=175$ into the formula: $x^{2}=55\times175$. $x^{2}=9625$.

Step3: Solve for $x$

Take the square - root of both sides: $x=\sqrt{9625}\approx98.11$. Rounding to the nearest unit, $x\approx98$.

Answer:

98 units