1.

If S, S_(1), S_(2) be the circles of radii 5, 3, 2 respectively. If S_(1) and S​_(2) touch externally and they touchinternally with S. The radius of circle S_(3) which touches externally with S_(1) and S​_(2) and internally with Sis :

Answer»

`(30)/(19)`
`(12)/(7)`
`(5)/(4)`
Can't be DETERMINED

Solution :For diagram we get
`(r+2)^(2)+(r+3)^(2)3`
`=2.3^(2)+3.2^(2)+5(5-r)^(2)`
`rArr 76r = 120`
`rArr r = (120)/(76)`
`rArr r = (30)/(19)`


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