Since , segment AB ≅ segment BC as their arcs are congruent ; therefore , ΔABC is an isosceles triangle .
Properties of a circle :
If a circle is circumscribed around a triangle, then the vertices of the
1. Triangle divides the circle into three arcs
2. The three sides of the triangle are the chords of the circle
3. Each chord in the circle subtended by an arc
4. If two arcs equal, then they are subtended equal chord
∵ 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.
To learn more on circle properties :
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