What are the coordinates of the center of the circle that passes through the points (1, 1), (1, 5), and (5, 5)? a. (0, 0) b. (5, 1) c. (3, 3) d. (2.5, 2.5)

let the distance between center and point (5,5) = d₁

let the distance between center and point (1,5) = d₂

let the distance between center and point (1,1) = d₃

The condition of the circle is d₁ = d₂ = d₃

Making two equations to find x , y

d₁² = d₂²

∴ (x-5)² + (y-5)² = (x-1)² + (y-5)²

∴ (x-5)²  = (x-1)²

∴ x-5 = \pm (x-1) ⇒⇒⇒ positive sign unacceptable

∴ x-5 = -(x-1)

∴ x = 3

d₁² = d₃²

∴ (x-5)² + (y-5)² = (x-1)² + (y-1)²

substituting with x and simplifying the equation

∴ y = 3

∴center = (3,3)

 The correct choice will be (C)

Answer ⇒⇒⇒ C. (3, 3)

Robin is winning the game and the explanation for the answer is :

Step-by-step explanation:

core represents the number of centimeter each player is away from the center. Given the mean of Robin = 107 and mean of Evelyn = 138

And, as it is mentioned that the player whose object lands more close to the center wins the game.

Evelyn has the greater mean. It indicates that, on average, Evelyn objects landed farther away from the center than Robin's.

Therefore, this difference means that Robin is winning the game.