Answer:
The true statement is " They are concentric circles " ⇒ A
Step-by-step explanation:
Concentric circles are the circles that have same center and different radii
Internally tangent circles are the circles that touch each other in one point and one of them is inside the other
Congruent circles are the circles that have same radii
The equation of the circle that its center is the origin and its radius is r is x² + y² = r²
∵ The equation of circle A is x² + y² = 4
∴ Its center is the origin
∵ r² = 4 ⇒ take √ for both sides
∴ r = 2
∴ Its radius is 2 units
∵ The equation of circle B is x² + y² = 25
∴ Its center is the origin
∵ r² = 25 ⇒ take √ for both sides
∴ r = 5
∴ Its radius is 5 units
∵ The two circles have the same center (origin)
- That means they are NOT internally tangent circles but they are
concentric circles
∵ The two circles have different radii
- That means they are NOT congruent circles
∵ The difference between their radii = 5 - 2 = 3
- That means the difference between their radii is NOT 21
∴ The two circles are concentric
The true statement is " They are concentric circles "
