Question

Calcular o Raio do círculo da figura anexa

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a^2 = b^2 + c^2}$

$\mathsf{2^2 = \left(\dfrac{3}{2}\right)^2 + h^2}$

$\mathsf{h^2 = 4 - \dfrac{9}{4} = \dfrac{16 - 9}{4} = \dfrac{7}{4}}$

$\mathsf{h = \dfrac{\sqrt{7}}{2}}$

$\mathsf{R^2 = (R - h)^2 + \left(\dfrac{3}{2}\right)^2}$

$\mathsf{R^2 = (R - \dfrac{\sqrt{7}}{2})^2 + \left(\dfrac{3}{2}\right)^2}$

$\mathsf{R^2 = (R^2 - R\sqrt{7} + \dfrac{7}{4}) + \left(\dfrac{9}{4}\right)}$

$\mathsf{4R^2 = 4R^2 - 4R\sqrt{7} + 7 + 9}$

$\mathsf{4R^2 = 4R^2 - 4R\sqrt{7} + 16}$

$\mathsf{R^2 = R^2 - R\sqrt{7} + 4}$

$\mathsf{R^2 + R\sqrt{7} = R^2 + 4}$

$\mathsf{R\sqrt{7} = 4}$

$\boxed{\boxed{\mathsf{R = \dfrac{4\sqrt{7}}{7}}}}$