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Problema Proposto
35 - Dados os pontos colineales e consecutivos
A, B. Cy D sabe-se que: AC= 8 e BD=4.
Calcular BC, se :
2. (AC).(CD)+ (AB).(BD)= 4.(BC).(BC .

[tex3]\mathsf{
AB = x\\
BC = y\\
CD = z\\
x+y=8\\
y+z = 4\implies z= 4-y\\
\therefore x - z = 4\implies x = 4+z\\
2(x+y).z+x(y+z) = 4y^2\implies 4z+x = y^2\\
Substiutindo: 4z+z+4 =y^2 \implies 5z+4 = y^2 \implies 5(4-y)+4 = y^2\\
\therefore y^2+5y-24 = 0 \implies \boxed{\color{red}y =BC= 3}\\


}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{
AB = x\\
BC = y\\
CD = z\\
x+y=8\\
y+z = 4\implies z= 4-y\\
\therefore x - z = 4\implies x = 4+z\\
2(x+y).z+x(y+z) = 4y^2\implies 4z+x = y^2\\
Substiutindo: 4z+z+4 =y^2 \implies 5z+4 = y^2 \implies 5(4-y)+4 = y^2\\
\therefore y^2+5y-24 = 0 \implies \boxed{\color{red}y =BC= 3}\\


}[/tex3]