A six-pointed star is drawn inside a circle, and the three long diagonals of the hexagon in its middle are drawn. How many triangles are there in the figure?

6 small triangles around the centre, 6 star points, and the 2 big triangles that make the star: 14. Each diagonal also cuts off 2 medium triangles (a star point together with the half-hexagon next to it): $3\times 2=6$. Total $14+6=20$.