Noah is baking a two-layer cake, in which the bottom layer is a circle and the top layer is a triangle. If segment AB = 10 inches and arc AB ≅ arc AC, what does Noah know about the top layer of his cake?

Question

Circumscribed circle D around triangle ABC, arcs AB and AC are congruent.

segment AB is twice the length of segment AC because their arcs are congruent; therefore, ΔABC is an isosceles triangle.
segment AB ≅ segment AC because their arcs are congruent; therefore, ΔABC is an isosceles triangle.
segment AB is twice the length of segment AC because their arcs are congruent; therefore, ΔABC is an equilateral triangle.
segment AB ≅ segment AC because their arcs are congruent; therefore, ΔABC is an equilateral triangle.

Answer 1

Based on the information provided, since arc AB is congruent to arc AC, it implies that the lengths of the segments that subtend these arcs (which are segments AB and AC) are also equal.

Thus, since arc AB ≅ arc AC, we can conclude that:

• Segment AB ≅ segment AC because their arcs are congruent; therefore, ΔABC is an isosceles triangle.

This statement is correct, as in an isosceles triangle, at least two sides are of equal length, and in this case, segments AB and AC are the equal sides of triangle ABC.