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A triangle ABC with vertices A = (2,5), ...

A triangle `ABC` with vertices `A = (2,5), B = (5,2)` and `C=(-1,-1)` inscribed on the curve `xy - x-y-3= 0` and `H= (alpha, alpha)` is orthocentre. Let `D, E` and `F` be the feet of perpendiculars from `A, B` and `C` on `BC, CA` and `AB` respectively and inradius of `DEF` is `r` then

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