b)12
c)24
d)25
e)28
c
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Obrigado, meu amigo!petras escreveu: ↑24 Mai 2022, 11:06 Flavio2020, geobson,
Aproveitando a ideia do geobson
[tex3]\mathrm{OH = x\implies r = 2x\\
\triangle AA'F \sim ABC \implies \frac{x}{76} = \frac{AA'}{95} \therefore AA' =\frac{5x}{4}\implies A'F = \frac{3x}{4} \\
\triangle CC'D \sim ABC \implies \frac{x}{57} = \frac{CC'}{95} \therefore CC' =\frac{5x}{3}\implies C'D = \frac{4x}{3} \\
\triangle A'BC': r = \frac{b+c-a}{2} \implies 2r = (57+\frac{5x}{4}+(76+\frac{5x}{3})-(95+\frac{3x}{4}+\frac{4x}{3})\\
4x = 38+\frac{x}{2}+\frac{x}{3}\implies 24x =228+5x \therefore \boxed{x = 12}\color{green}\checkmark
}[/tex3]