Question

un triunghi echilateral si un hexagon sunt inscrise in acelasi cerc C(O,R) . daca A3 = 72 radical 3 , aflati
a.R
b.l3
c.a6

Answer 1

$\it \mathcal{A}_{\triangle} = \dfrac{\ell^2\sqrt3}{4} =72\sqrt3 |_{:\sqrt3} \Longrightarrow \dfrac{\ell^2}{4} =72 \Longrightarrow \ell^2= 4\cdot72 =4\cdot36\cdot2$

$\it \Longrightarrow \ell = 12\sqrt2 cm$

$\it R = \dfrac{\ell\sqrt3}{3}$

$\it \ell_6 = R,\ \ a_6 = \dfrac{R\sqrt3}{2}$

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