Derive the equation of a circle from center/radius and complete the square to identify center/radius.
Find a missing parameter in a circle equation
Problem
Find the missing parameter in \((x-2)^2+(y-1)^2=r^2\) given that point \((5,5)\) lies on the circle.
Big Picture
What this problem is really about
The point-on-circle condition turns the missing radius into a distance calculation. We’ll substitute the boundary point into the shifted squares, evaluate the horizontal and vertical differences, combine their squares to obtain radius squared, and take the nonnegative root because the requested parameter is a geometric length.
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