If the line y=mx+c is a tangent of a circle x^2 +y^2 =r^2 . Show that, c^2 =r^2 (1+m^2 )


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Question Number 170458 by MathsFan last updated on 24/May/22

$I f t h e l i n e y = m x + c i s a t a n g e n t o f$ $a c i r c l e x^{2} + y^{2} = r^{2} . S h o w t h a t,$ $c^{2} = r^{2} (1 + m^{2})$
	Answered by greougoury555 last updated on 24/May/22

	$\Rightarrow r = \frac{∣ c ∣}{\sqrt{1 + m^{2}}}$ $\Rightarrow r^{2} = \frac{c^{2}}{1 + m^{2}}$ $\Rightarrow c^{2} = (1 + m^{2}) r^{2}$
	Commented by MathsFan last updated on 24/May/22

	$t h a n k y o u s i r$
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