In \(\triangle ABC \), \(\overline{AB} = 8, \overline{BC} = 15, \overline{AC} = 12 \). Two tangent circles are to be inscribed in the triangle as shown in the figure above. They are both tangent to \( BC \), with the left one tangent to \( AB \), while the right one is tangent to \( AC \). If \( S_\text{min} \) is the minimum sum of the areas of the two circles , enter \( \lfloor 10^5 S_\text{min} \rfloor \)
by
Hosam Hajjir
