Question

A line segment joins points upper B and upper C. A line with arrows at both ends passes through the center point upper A and extends beyond the circle. It intersects and is perpendicular to line segment upper B upper C. Two right angle marks are drawn at the point of intersection, which is labeled as point upper D. Line segment upper A upper B joins those two points, and line segment upper A upper C joins those two points, to form triangle upper A upper B upper C.

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

(1 point)
Responses

>
>

greater than

≥
≥

greater than or equal to

<
<

less than

≤

Answer 1

AB + AC > BC

Reason: AB = AC = radius r, so AB + AC = 2r. BC is a chord shorter than the diameter (2r), so 2r > BC. Thus AB + AC > BC.