Centre of a Circle Tangent to Two Lines and Passing Through a Point

Centre of a Circle Tangent to Two Lines and Passing Through a Point

The centre must satisfy equal-distance conditions:

$$\frac{|A_1h+B_1k+C_1|}{\sqrt{A_1^2+B_1^2}}=\frac{|A_2h+B_2k+C_2|}{\sqrt{A_2^2+B_2^2}}$$

and the circle through $$(x_1,y_1)$$ satisfies:

$$(x_1-h)^2+(y_1-k)^2=r^2$$

Usage

- Used to determine circles satisfying simultaneous tangency and point-passing conditions.