Three point define a circle
Q1. Three point define a circle
Use circum-center theory
- Draw a large triangle ABC
- Draw bisectors of sides
- Bisectors meet at I which is the cicum-center
- Radius = IA = IB = IC
- Draw circle using center I and radius IA
Q2. Find equation of circle
- Circle equation : x^2 + y^2 + a*x + b*y + c
- Substitute points into equation and we have 3 linear equation
- Solve 3 linear equations and get a, b, c
- Use completing the square to changle equation to standard form
- Standar form : (x - h)^2 + (y - k)^2 = r^2