AIME II 2009 #5

[stupidityismygam]

Equilateral triangle [unparseable or potentially dangerous latex formula] is inscribed in circle [unparseable or potentially dangerous latex formula] which has radius [unparseable or potentially dangerous latex formula] Circle [unparseable or potentially dangerous latex formula] with radius [unparseable or potentially dangerous latex formula] is internally tangent to circle [unparseable or potentially dangerous latex formula] at one vertex of [unparseable or potentially dangerous latex formula] Circles [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] both with radius [unparseable or potentially dangerous latex formula] are internally tangent to circle [unparseable or potentially dangerous latex formula] at the other two vertices of [unparseable or potentially dangerous latex formula] Circles [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are all externally tangent to circle [unparseable or potentially dangerous latex formula] which has radius [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are relatively prime positive integers. Find [unparseable or potentially dangerous latex formula]

[sinkokuyou]

I have the picture though:

[sinkokuyou]

so I guess if the radius is r
then use the cosine law:
[unparseable or potentially dangerous latex formula]
then u get [unparseable or potentially dangerous latex formula], so m+n=27+5=32
Is that the answer?

[stupidityismygam]

yes