# Find the locus of ce

Given: Circles with centres O, O', O" touching line T at P.
To prove: To find the locus of centres of circles which touch a given line at a given point.

Proof: As OP, O'P, O''P are the radii of the circles touching line T at P, it is perpendicular to the given line.
∴ OP, O'P, O''P represent the same straight line passing through P and ⊥ to PT.
Hence the locus of the centres of circles which touch a given line at a given point is a straight line to the given line at the given point.

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