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Como [tex3]\angle AOB = 120^{\circ}[/tex3]
, a lei dos cossenos no [tex3]\triangle AOB[/tex3]
diz que:
[tex3]AB^2 = 2R^2 + 2R^2 \cdot \frac 12 = 3R^2 \implies AB = R \sqrt3[/tex3]
Potência de [tex3]M[/tex3]
:
[tex3]1 \cdot (2R-1) = 2 \cdot (R \sqrt3 - 2) \iff 2R -1 = 2R\sqrt3 - 4 \iff R = \frac3{2(\sqrt3-1)} = \frac{3(\sqrt3+1)}4[/tex3]
φως εσύ και καρδιά μου εγώ πόσο σ' αγαπώ.