Let ABC be a triangle. The angle bisectors AD, BE, and CF meet at I, so that DI = 3, BD = \(\sqrt{7}\), and BI = 4. Compute the area of triangle ABC.

Here's a similar problem :

https://web2.0calc.com/questions/pls-help_10037

This one doesn't work though.

There isn't a triangle ABC that fits the given lengths.