Question

The sides of ∆ABC inscribed in a circle are equidistant from the center. Tricia says that ∆ABC must be equilateral. Which explains whether Tricia is correct?

Answer 1

Tricia is correct because the sides of the triangle are congruent since they are equidistant from the center of the circle.

Explanation:

Given that the sides of ΔABC inscribed in a circle are equidistant from the center. This implies the triangle is drawn within the circumference of the circle with a center.

Bisecting the three sides of the triangle shows that the three bisectors intersect at a point which is the center of the circle, and the lines are equidistant to this point. This proves that the length of the sides of the triangle are equal, so that the triangle is an equilateral triangle. Therefore, Tricia's statement is correct.