Locus of Centres of Circles Touching Two Parallel Lines

Rarely Tested

Locus of Centres of Circles Touching Two Parallel Lines

For:

$$Ax+By+C_1=0$$

and:

$$Ax+By+C_2=0$$

the centres of circles tangent to both lie on:

$$Ax+By+\frac{C_1+C_2}{2}=0$$

Usage

- Used to find the centre locus for circles tangent to two parallel lines.

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