Since d=2r, r=d/2 so
r=√(x^2/2), since x=8
r=4√2 in (exact)
r≈5.66 in (to nearest hundredth of an inch)
Find the radius of a circle in which an inscribed square has a side of 4 inches.
from the picture you see that the radius is 1/2 of the square side.
4 : 2 = 2 inches
2 inches is your answer
The diagonal of the square is the radius of the circle. To find the diagonal, you can draw a line between 2 opposite points of the square to split the square into 2 equal triangles. As they are right triangles and have 2 equal sides, they are 1-1-√2 triangles, or 45-45-90 (degrees). The length of the 2 equal sides of the triangle is 4 inches, to multiplying that by √2 will give 4√2 inches, which is the radius of the circle.
The radius is 5.65 inches.
A diagonal of an inscribed square, is also the hypotenuse of an isosceles right triangle with two sides of the square as legs and it is also the diameter of the circle.
Here, the side of the square is 8 inches.
We have to find the diagonal with both legs 8 inches.
According to Pythagoras theorem, let the diagonal or hypotenuse be x
x = √128
x = 11.31
So, this is the diameter of the circle.
The radius will be inches
Hence, the radius is 5.65 inches.
radius is 4√2
i use my brain for prombles like this maybe you could try it