Find the number of triangles in the given figure.

Concept: When counting triangles in a figure built from intersecting chords, first identify every triangle bounded directly by the drawn line segments — these are the elementary (simple) triangles. Then identify every larger triangle formed by joining two or more elementary triangles along a shared segment, provided its own three sides are actually drawn lines. The total number of triangles is the sum of both groups.

Application: Label the figure as shown: A, B, C, D, E lie on the circle with F below chord AE, and G is the point where the two diagonals AC and BE cross inside quadrilateral ABCE.

Simple (elementary) triangles — six in total:

• ABG, BCG, CGE and AGE — the four triangles formed inside quadrilateral ABCE where its two diagonals AC and BE cross at G.

• CDE — bounded by sides CD, DE and diagonal CE.

• AEF — bounded by sides AF, FE and side EA.

Composite triangles — four in total, each formed by joining exactly two of the four elementary triangles inside ABCE across point G (G lies on only one side of each, so a single line splits it into two parts, not three):

Total = 6 simple + 4 composite = 10 triangles.

Cross-check: A quadrilateral with both diagonals drawn always contains exactly 8 triangles (the 4 elementary ones plus the 4 formed by one full diagonal with two sides), so ABCE alone accounts for 8. CDE and AEF sit outside ABCE and share no interior lines with it, adding 2 more independent triangles. 8 + 2 = 10, confirming the count.