Circle Touching a Line at a Given Point

Rarely Tested

Circle Touching a Line at a Given Point

For the line:

$$Ax+By+C=0$$

touching the circle at $$(x_1,y_1)$$, the centre $$(h,k)$$ lies on:

$$B(h-x_1)-A(k-y_1)=0$$

Usage

- Used to restrict the centre to the normal through the point of contact.

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