Find the number of triangles in the given figure.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16
The figure is a triangle with three lines from each corner to the middle of the opposite side, all meeting at one point G. Naming the points lets every triangle be counted once, by size.
Smallest triangles around G (6): AFG, AGE, BFG, BGD, CDG, CEG
Two small triangles joined, with G as a corner (3): ABG, BCG, CAG
Half of the big triangle, cut off by one line (6): ABD, ACD, BAE, BCE, CAF, CBF
The whole triangle (1): ABC
Total \(=6+3+6+1=16\) triangles.
Tip: A triangle cut by three lines from its corners that meet at one inside point always has 16 triangles; the figure is common in papers, so the result is worth knowing.