Estude! Com Prof. Caju

Na figura, se AP = 1m e PQ = 8m calcular AC.
A) 2[tex3]\sqrt{2}m[/tex3]
B) 3m
C) 3[tex3]\sqrt{2}m[/tex3]
D) 2[tex3]\sqrt{3}m[/tex3]
E) 4m

[tex3]\mathsf{
△APH \sim △AQB \implies AH=\frac{9}{2R}\\
\triangle CHO: CH^2=CO^2−OH^2=R^2−(R−AH)^2=R^2−(R−\frac{9}{2R})^2\\
\triangle ACH : AC^2=AH^2+CH^2=(\frac{9}{2R})^2+R^2−(R−\frac{9}{2R})^2=\\
(\frac{9}{2R})^2+R^2−R^2+9−(\frac{9}{2R})^2=9 \therefore \boxed{AC=3}
}[/tex3]
(Soução:LuisFuentes-adapada)