Question

is the following statement a good definition? a pair of congruent circles is a pair of circles that have the same circumference. yes no

Explanation:

To determine if the definition is good, recall the formula for the circumference of a circle, \( C = 2\pi r \) (or \( C=\pi d \), where \( r \) is the radius and \( d \) is the diameter). If two circles have the same circumference, then \( 2\pi r_1=2\pi r_2 \), which implies \( r_1 = r_2 \). Congruent circles are defined as circles with the same radius (or diameter), so having the same circumference is equivalent to having the same radius, meaning the circles are congruent. The definition is reversible (if two circles are congruent, they have the same circumference, and if they have the same circumference, they are congruent) and clearly defines congruent circles in terms of a measurable property (circumference) that uniquely determines their congruence.

Answer:

yes