Explicație pas cu pas:
T.P. în ΔADC dreptunghic:
DC² = AC² - AD² = 8² - (6,4)² => DC = 4,8 cm
BC = 2•DC => BC = 9,c cm
a)
[tex]\sin (B) = \frac{AD}{AB} = \frac{6.4}{8} = 0.8 \\ [/tex]
[tex]\frac{AC}{ \sin(B) } = 2R \iff \frac{8}{0.8} = 2R \\ 2R = 10 \implies \boxed { \red {\bf R = 5}}[/tex]
b) AB = a, AD = b
[tex]\sin (B) = \frac{b}{a} \\ [/tex]
[tex]\frac{AC}{ \sin(B) } = 2R \iff \frac{a}{ \frac{b}{a} } = 2R \\ \frac{ {a}^{2} }{b} = 2R \implies \boxed { \red {\bf R = \frac{ {a}^{2}}{2b} }}[/tex]
c)
[tex]Aria_{\Delta ABC} = \frac{AD \cdot BC}{2} = \frac{6.4 \cdot 9.6}{2} = \\ = \bf 30.72 \: {cm}^{2} [/tex]
