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In triangle ABC, prove that the maximum ...

In triangle ABC, prove that the maximum value of `tan(A/2)tan(B/2)tan(C/2)i s R/(2s)`

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`tan(A/2)tan(B/2)tan(C/2)`
`sqrt(((s-b)(s-c))/(s(s-a)))sqrt(((s-a)(s-c))/(s(s-b)))sqrt((s-a)(s-b))/(s(s-c)`
`sqrt((s(s-a)(s-b)(s-c))/s^4`
`/_/s^2=r/s<=R/(2s)`.
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