Answer:
segment AB ≅ segment BC because their arcs are congruent; therefore, ΔABC is an isosceles triangle
Step-by-step explanation:
* Let's revise some facts in the circle- If a circle is circumscribed around a triangle, then the vertices of the triangle divide the circle into three arcs- The three sides of the triangle are the chords of the circle,
Each chord in the circle is subtended by an arc-
If two arcs are equal, then they are subtended as equal chords*
Let's solve the problem,
Circumscribed circle D around triangle ABC,
The vertices of triangle ABC lie on the circumference of the circle AB, BC, AC are the chords of the circle,
Arcs AB and AC are congruent,
Arc AB ≅ arc AC, Arc AB subtended the chord AB, Arc AC subtended the chord AC, AB = AC, AB = 6 inches, AC = 6 inches,
The triangle with two equal sides is called an isosceles triangle, Δ ABC is an isosceles triangle,
Noah knows that the top layer of his cake is an isosceles triangle* segment AB ≅ segment BC because their arcs are congruent; therefore, ΔABC is an isosceles triangle.
segment AB ≅ segment BC because their arcs are congruent; therefore, ΔABC is an isosceles triangle ⇒ answer D.
