Clawson Point with max Area

Find the maximum area, $A_{\max}$ , of a triangle in which the Clawson Point is a distance of 3, 4, and 5 units from the triangle's vertices. Submit $\lfloor 10^4 A_{\max}\rfloor$ .

Inspiration

Bonus. Exist triangle area $A$ with a Clawson point distance of 3, 4, and 5 units from the triangle's vertices, that $A_{\min} \lt A \lt A_{\max}$ ?