Question

The equation of ⊙ is 2+2=4. The equation of ⊙ is 2+2=25. What do you know about the two circles? Select the true statement.

Answer 1

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 "