In right $\triangle ABC$, shown here, $AB = 15 \text{ units}$, $AC = 24 \text{ units}$ and points $D,$ $E,$ and $F$ are the midpoints of $\o

[ABC] = 180 square units

[DEF] = ¹/₄ [ABC]  = 45 square units

[DEF] : [ABC] = 1 : 4

∠ABC = tan^-1(AC / AB)

BC = sqrt(AB² + AC²) = √801

ΔABC inradius  r = 5.349

ΔABC circumradius   R = 14.151