Answer:
segment AB ≅ segment BC because their arcs are congruent; therefore, ΔABC is an isosceles triangle ⇒ answer D
Step-by-step explanation:
* Lets 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 subtended by an arc
- If two arcs equal, then they are subtended equal chords
* Lets 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 know 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.
