Question

Find the center of the circle that can be circumscribed about ABC with A(0,0) B(6,0) C(6,4)

Answer 1

This can be solved by the distance formula.
If the center of the circle is at (h,k)
r² = (h - 0)² + (k - 0)²
r² = (h - 6)² + (k - 0)²
r² = (h - 6)² + (k - 4)²

Equating the equations
h² + k² = (h - 6)² + k²
h = 3

(h - 6)² + k² = (h - 6)² + (k - 4)²
k = 2

Therefore, the center of the circle is at (3,2).