Question

Calcula AC, si el radio mide 4 cm. ​

Answer 1

Verified answer

Respuesta:

         [tex]26cm[/tex]

Explicación paso a paso:

[tex]AB= c = ?[/tex]

[tex]AC = b = ?[/tex]

[tex]BC = a = 10cm[/tex]

[tex]Rario: r = 4cm[/tex]

[tex]b^{2} =c^{2} +a^{2} ,entonces: b^{2} = c^{2} + 10^{2}[/tex]

[tex]r = \frac{a+c-b}{2} ,entonces: 4 = \frac{10+c-b}{2}[/tex]

[tex]b^{2} -c^{2} =100,entonces: (b+c)(b-c) = 100[/tex]

[tex]2(4) = 10+c-b, entonces: b-c = 10-8[/tex]

[tex](c+b) (10-8 ) = 100,entonces: 2c+2b= 100[/tex]    [tex]ecuac.1[/tex]

[tex]b-c = 10-8, entonces: b-c = 2[/tex]                   [tex]ecuac.2[/tex]

[tex]Por -reduccion:[/tex]

[tex]2b+2c = 100[/tex]

[tex]2b-2c = 4[/tex]

______________

[tex]4b[/tex]         [tex]= 104[/tex]

[tex]b = \frac{104}{4}[/tex]

[tex]b= 26cm[/tex]

[tex]Luego: b = AC = 26cm[/tex]

[tex]AC = 26cm[/tex]