Find the locus of the centres of circles which touch a given line at a

1.	Find the locus of the centres of circles which touch a given line at a given point.
Answer» Let APB be the given line, and let a circle with centre O touch APB at P.Then, {tex}\\angle O P B{/tex}= 90°. Let there be another circle with centre O\' which touches the line APB at P.Then, {tex}\\angle O ^ { \\prime } P B{/tex}=90°.This is possible only when O and O\' lie on the same line O\'OP. Hence,the required locus is a line perpendicular to the given line at the point of contact.

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