The round hole in the square machine part is an inscribed circle
The equation of the circle is [tex](x - 2)^2 + (y - 2)^2 = 1[/tex]
The corner of the square machine part is said to be at the origin.
This means that, the coordinates of the machine parts are:
(x,y) = (0,0), (4,0), (4,4) and (0,4)
Calculate the midpoint of the diagonals, to determine the midpoint of the circle.
(x,y) = 0.5 * (0 + 4, 4 + 0)
This gives
(x,y) = (2,2)
The diameter of the circle is:
d = 2 inches
Divide by 2 to calculate the radius
r = 1 inch
The equation of a circle is represented as:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Where:
Center = (x,y) = (a,b) = (2,2)
So, we have:
[tex](x - 2)^2 + (y - 2)^2 = 1^2[/tex]
Evaluate the square of 1
[tex](x - 2)^2 + (y - 2)^2 = 1[/tex]
Hence, the equation of the circle is [tex](x - 2)^2 + (y - 2)^2 = 1[/tex]
Read more about circle equations at:
https://brainly.com/question/1559324
