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Find the locus of the centres …

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

Posted by Abc Pqr 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

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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CBSE > Class 10 > Mathematics