Question

O lado do quadrado vale 4 cm. Qual é o valor do raio de uma das circunferência menores?

Answer 1

2 ( R - r )^2 = ( R + r )^2

R^2 - 6Rr + r^2 = 0

4 - 12r + r^2 = 0

ou

r^2 - 12r + 4 = 0

r = 6 - 4\/2

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(L/2 + r)^2 = (L/2 - r)^2 + (L/2 - r)^2}$

$\mathsf{(2 + r)^2 = (2 - r)^2 + (2 - r)^2}$

$\mathsf{4 + 4r + r^2 = (4 - 4r + r^2) + (4 - 4r + r^2)}$

$\mathsf{4 + 4r + r^2 = 8 - 8r + 2r^2}$

$\mathsf{r^2 - 12r + 4 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-12)^2 - 4.1.4}$

$\mathsf{\Delta = 144 - 16}$

$\mathsf{\Delta = 128}$

$\mathsf{r = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{12 \pm \sqrt{128}}{2} \rightarrow \begin{cases}\mathsf{r' = \dfrac{12 + 8\sqrt{2}}{2} = 6 + 4\sqrt{2}}\\\\\mathsf{r'' = \dfrac{12 - 8\sqrt{2}}{2} = 6 - 4\sqrt{2}}\end{cases}}$

$\boxed{\boxed{\mathsf{r = 6 - 4\sqrt{2}\:cm}}}$