Use the image to answer the question.

Question

A circle has a center point upper A. Points upper B and upper C lie opposite each other on the circumference to the right of upper A.

Use what you know about radii, chords, and diameters to identify the correct inequality. In Circle A
, AB+AC______BC
.

(1 point)
Responses

<
less than

>
greater than

≥
greater than or equal to

≤

Answer 1

In a circle, the diameter is the longest chord. Points B and C are opposite each other on the circumference, meaning that segment BC is a diameter.

According to the triangle inequality theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. In this case, segments AB and AC are each radii of the circle.

Since \( AB \) and \( AC \) are both radii, and segment \( BC \) is a diameter, we can conclude that:

\[ AB + AC > BC. \]

Therefore, the correct inequality is:

AB + AC > BC.

So the answer is: > (greater than).