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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

>
greater than

≥
greater than or equal to

<
less than

≤

1 answer

In Circle A, points B and C lie on the circumference, and since they are opposite each other, the line segment BC is a diameter of the circle. The segments AB and AC are both radii of the circle.

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 third side.

In this case, considering triangle ABC:

  • AB + AC (the sum of the lengths of the two radii) must be greater than BC (the length of the diameter).

Thus, we have:

AB + AC > BC

So the correct inequality is:

AB + AC > BC.

The response is:

(greater than)