Segment AB ≅ segment BC because their arcs are congruent; therefore, ΔABC is an isosceles triangle.
What is an isosceles triangle?
The isosceles triangle is the triangle in which the two sides are equal and the two opposite angles are also equal.
If a circle is circumscribed around a triangle, then the vertices of the
Triangle divides 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.
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