Pitágoras no [tex3]\Delta IMN[/tex3]
:
[tex3]R^2 = \left(\frac{l_4}{2}\right)^2 + \left(\frac{l_4}{2}\right)^2[/tex3]
[tex3]R = \frac{l_4}{2}.\sqrt{2}[/tex3]
[tex3]l_4 = R\sqrt{2}[/tex3]
No [tex3]\Delta PMO[/tex3]
:
[tex3]sin \ 30 = \frac{\frac{l_6}{2}}{R}[/tex3]
[tex3]\frac{1}{2} = \frac{l_6}{2R}[/tex3]
[tex3]l_6 = R[/tex3]
Pitágoras no [tex3]\Delta PMO[/tex3]
:
[tex3]R^2 = \left(\frac{l_4}{2} + d\right)^2 + \left(\frac{l_6}{2}\right)^2[/tex3]
[tex3]R^2 = \left(\frac{R\sqrt{2}}{2} + d\right)^2 + \left(\frac{R}{2}\right)^2[/tex3]
[tex3]\frac{3R^2}{4} = \left(\frac{R\sqrt{2}}{2} + d\right)^2[/tex3]
[tex3]\frac{\sqrt{3}R}{2} = \frac{R\sqrt{2}}{2} + d[/tex3]
[tex3]d = \frac{(\sqrt{3}- \sqrt{2})}{2}R[/tex3]