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: Apply the tangent - secant theorem

The tangent - secant theorem states that if a tangent segment \(BA\) and a secant segment \(BD\) are drawn to a circle from an external point \(B\), then \(BA^{2}=BC\times BD\).
We know that \(BC = 55\) and \(BD=BC + CD=55 + 120=175\).

Step2: Calculate \(BA\)

Substitute the values into the formula \(x^{2}=55\times175\).
First, calculate \(55\times175=(50 + 5)\times175=50\times175+5\times175 = 8750+875=9625\).
Then, \(x=\sqrt{9625}\approx98.11\).

Answer:

\(98\) units