1009.11 – Triangle Count

Count carefully; be systematic! The triangle $\triangle AEF$ has four more like it, $\triangle BAG, \triangle CBH, \triangle DCJ$, and $\triangle EDK$, moving around the large figure clockwise. Similarly the seven additional triangles $\triangle AFB, \triangle AEB, \triangle ADH, \triangle AKC, \triangle ADC$, and $\triangle AFG$ (all containing vertex $A$) each has four more around the large figure.

So the total number is $8 \times 5 = 40$. (Have we counted anything twice? Have we missed any?)