Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) Circles radii 5, 5 and 8 are mutually extremally tangent. If a fourth circle of radius r touches all the three circles externally, then the value of r is numbers. - Sarthaks eConnect

Circles radii 5, 5 and 8 are mutually extremally tangent. If a fourth circle of radius r touches all the three circles externally, then the value of r is numbers.

Circles radii 5, 5 and 8 are mutually extremally tangent. If a fourth circle of radius r touches all the three circles externally, then the value of r is numbers.

A.

1

B.

`7/8`

C.

`8/9`

D.

`9/11`

Solution

0 votes

Best answer

From the figure, 12 = x + r + 8

`=> 12=sqrt((x+5)^2-25)+r+8`

`=>12=sqrt(r^2+10r)+r+8`

`=>(4-r)^2=r^2+10`

`=>18r=16`

`r=8/9`