Question

This diagram is a straightedge and compass construction. \(A\) is the center of one circle, and \(B\) is the center of the other. Explain how we know triangle \(ABC\) is equilateral.

Two congrent circles intersect. Left circle center A, right circle center b. Cirlces intersect at point C. Segments A B, B C and A C are drawn.

Answer 1

Triangle ABC is equilateral because each segment is a radius of congruent circle

How to find that the triangle is equilateral

The two circles are congruent, this means that the radius are equal. Therefore distance from A to B is radius makin the base.

The sides also constitute measurements made using constant radius.

Since the circle is congruent, the radius will trace equal sides of the triangle