Question

Two circles in the coordinate plane with congruent radii intersect in exactly two points. Why is it not possible for these circles to be concentric?

Answer 1

Circles having same center are called concentric Circles.

And circles having same radii are called congruent circles.

Now, coming to the question

Two circles in the coordinate plane with congruent radii intersect in exactly two points.These are congruent circles so, Maximum number of point of intersection of two circles can be either , 0 , 1 and maximum of 2 points.

When circles are concentric, their will be no point of intersection that is the two circles will never intersect.

These circles can't be concentric because concentric circles never intersect .The point of intersection of two concentric circles is None.

Answer 2

Two arcs are congruent if and only if their associated chords are congruent.

Explanation:

The associated radii of arcs are the radii of the circles the arcs are in. However, you can have two arcs in one circle that are not congruent. The circle would not have two different radii, but the arcs would not necessarily be congruent.