Question

1
select the correct answer from each drop-down menu.
segment \\(\overline{ab}\\) intersects the circle with center \\(c\\). what statement correctly describes the relationship shown in the image?
since the radius of the circle is \\(\overline{ab}\\), \\(\overline{ab}\\) is the circle.

Explanation:

Step1: Analyze the radius and AB

The radius (from C to the point of intersection) is perpendicular to \( \overline{AB} \). By the tangent - radius theorem, a line perpendicular to a radius at its outer endpoint is a tangent. Also, the radius is perpendicular to \( \overline{AB} \), so the radius is perpendicular to \( \overline{AB} \) (first drop - down: "perpendicular to").

Step2: Determine the relationship of AB to the circle

Since the radius is perpendicular to \( \overline{AB} \) at the point of contact, \( \overline{AB} \) touches the circle at exactly one point. So \( \overline{AB} \) is a tangent to the circle (second drop - down: "tangent to").

Answer:

First drop - down: perpendicular to; Second drop - down: tangent to