Question

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

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

Answer 1

i can insert a photo if you need

Answer 2

This would be a little tricky without some background in geometry, but the important part is that arcs AB and AC are congruent. That means they are the same size. The only way this can be true is if AB and AC are the same length.
Even if you don't know anything about arcs, maybe I can convince you that the distance from one end to the other end of the arc would be the same for two arcs of the same size?
All this to say that AB and AC do have the same length. What could you deduce from that?

Answer 3

wait omg that helps so much ahhh thank you!!!!

Answer 4

Great! Glad you understand better now