The radius of the circle passing through the points (-1, 1), (2, -1) and (1, 0) is

Steps to Solve

1. Find the general form of the circle's equation

The general form of the circle's equation is given by:
$$ (x - h)^2 + (y - k)^2 = r^2 $$
where $(h, k)$ is the center of the circle and $r$ is the radius.

2. Substitute the points into the equation

Given points are $(-1, 1)$, $(2, -1)$, and $(1, 0)$.
We will substitute these points into the general equation to create a system of equations.

3. Set up the equations

For each point, substitute $x$ and $y$ into the circle equation:

From $(-1, 1)$:
$$ (-1 - h)^2 + (1 - k)^2 = r^2 $$

From $(2, -1)$:
$$ (2 - h)^2 + (-1 - k)^2 = r^2 $$

From $(1, 0)$:
$$ (1 - h)^2 + (0 - k)^2 = r^2 $$

4. Expand the equations

Expand each equation:

1. For $(-1, 1)$:
   $$ (h + 1)^2 + (k - 1)^2 = r^2 $$

2. For $(2, -1)$:
   $$ (h - 2)^2 + (k + 1)^2 = r^2 $$

3. For $(1, 0)$:
   $$ (h - 1)^2 + k^2 = r^2 $$

4. Solve the system of equations

Subtract the first equation from the second and third and solve for $h$ and $k$.

6. Calculate the radius

Once you find $h$ and $k$, plug these values into any of the equations to find $r^2$, then take the square root to find $r$:
$$ r = \sqrt{r^2} $$