Two circle are externally tangent. Lines PAB and P A 'B ' are common tangents with A and A ' on the smaller circle and B and B ' on the larger circle. If PA=AB=4, then the square of the radius of the circle is___________

Answer

2

Explanation

`(AC_(1))/(PA)=(BC_(2))/(PB)`
`BC_(2)=2AC_(1)`
`PC_(1)=sqrt(16+r^(2))`
and `PC_(2)=sqrt(64+4r^(2))=2sqrt(16+r^(2))`
or `PC_(2)-PC_(1)=3r`
or `2 sqrt(16+r^(2))-sqrt(16+r^(2))=3r`
or `sqrt(16+r^(2))=3r`
or `16+r^(2)=9r^(2)`
or `r^(2)=2`