A circle {C_1} of radius 2 touches both x - a | vedclass

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Question

(b) First circle touches both axes and radius is $2$ unit.

Hence centre of circle is $(2, 2)$.

Let radius of other circle be a and this circle a

Vedclass · Accepted Answer

$6 + 4\sqrt 2 $

Vedclass · Answer

(b) First circle touches both axes and radius is $2$ unit.

Hence centre of circle is $(2, 2)$.

Let radius of other circle be a and this circle also touches both the axes.

Hence centre of circle is $(a, a).$

This circle touches first circle

Hence, $\sqrt {{{(a - 2)}^2} + {{(a - 2)}^2}} = a + 2$ squaring both the sides,${a^2} - 12a + 4 = 0$

$a = \frac{{12 \pm \sqrt {{{(12)}^2} - 4 	imes 4 	imes 1} }}{2}$

$ = \frac{{12 \pm \sqrt {128} }}{2} = 6 \pm 4\sqrt 2 $

But $a > 2$, Hence $a = 6 - 4\sqrt 2 $ is neglected

Hence, $a = 6 + 4\sqrt 2 $.

A circle ${C_1}$ of radius $2$ touches both $x$ - axis and $y$ - axis. Another circle ${C_2}$ whose radius is greater than $2$ touches circle ${C_1}$ and both the axes. Then the radius of circle ${C_2}$ is

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