Question

Calcula AC, si el radio mide 4 cm. ​

Answer 1

Respuesta:

         $26cm$

Explicación paso a paso:

$AB= c = ?$

$AC = b = ?$

$BC = a = 10cm$

$Rario: r = 4cm$

$b^{2} =c^{2} +a^{2} ,entonces: b^{2} = c^{2} + 10^{2}$

$r = \frac{a+c-b}{2} ,entonces: 4 = \frac{10+c-b}{2}$

$b^{2} -c^{2} =100,entonces: (b+c)(b-c) = 100$

$2(4) = 10+c-b, entonces: b-c = 10-8$

$(c+b) (10-8 ) = 100,entonces: 2c+2b= 100$    $ecuac.1$

$b-c = 10-8, entonces: b-c = 2$                   $ecuac.2$

$Por -reduccion:$

$2b+2c = 100$

$2b-2c = 4$

______________

$4b$         $= 104$

$b = \frac{104}{4}$

$b= 26cm$

$Luego: b = AC = 26cm$

$AC = 26cm$