Question

Find the radius of smallest circle ( which is colored yellow ) ..

Radius of Quadrant is 4cm. .

I want full solution please.

fake answers will be reported immediately.

Answer 1

Step-by-step explanation:

hey dear see the attachment of

Answer 2

$\large\tt{Question:-}$

Find the radius of smallest circle ...

$\Large\underline{\underline{\sf{Solution}:}}$

Refer to image First ....

First we solve value of R ( Radius of larger circle) ...

By pythagoras theoram in shaded ∆ ,

we can say that,,,

$\red{ (2 \sqrt{4R })^{2} + {R}^{2} = {(8 -R)}^{2} } \\ \\ \implies \: \green{16R + {R}^{2} = 64 + {R}^{2} - 16R} \\ \\ \implies \: 32R = 64 \\ \\ \implies \: \pink{ R = 2}$

Now,,,,

Let radius of smaller circle be x cm.

putting value of this and again using pythagoras theoram we get,,,,

${x}^{2} + (2 \sqrt{2x} + 2 \sqrt{8} )^{2} = (8 - x)^{2} \\ \\ \implies \: {x}^{2} + 8x + 32 + 32 \sqrt{x} = 64 + {x}^{2} - 16x \\ \\ \implies \: 8\sqrt{x} ( \sqrt{x} + 32) = 16(2 - x) \\ \\ \red{x = \frac{1}{9}}$

So, radius of smallest circle will be (1/9)cm ..