Question

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.
(there are also reset and next buttons shown, and a circle with center c, radius to the intersection point of ab, and ab with a right angle at the intersection with the radius)

Explanation:

Step1: Recall Tangent Properties

A tangent to a circle is perpendicular to the radius at the point of contact. Here, the radius (from center \( C \) to the point of contact) is perpendicular to segment \( \overline{AB} \) at the point of intersection with the circle.

Step2: Analyze Radius and \( \overline{AB} \)

The radius (let's say length \( r \)) is perpendicular to \( \overline{AB} \) at the point where \( \overline{AB} \) meets the circle. A line perpendicular to a radius at its outer endpoint is a tangent. So, the radius is perpendicular to \( \overline{AB} \), meaning \( \overline{AB} \) is a tangent to the circle. Also, the radius is perpendicular (not equal or parallel in length context here, but in terms of the tangent - radius relationship) to \( \overline{AB} \). Wait, the first drop - down is about the radius's relation to \( \overline{AB} \): the radius is perpendicular to \( \overline{AB} \). Then, since a line perpendicular to a radius at the point of contact is a tangent, \( \overline{AB} \) is tangent to the circle.

Answer:

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