How many triangles are formed when all the diagonals from one vertex of a hexagon are drawn?

How many triangles are formed when all the diagonals from one vertex of a hexagon are drawn?
  1. $3$
  2. $4$
  3. $5$
  4. $6$

Solution

From one vertex of an $n$-gon we get $(n-2)$ triangles. For a hexagon ($n=6$): $6-2 = 4$ triangles.

Asked in: IMO

Practice more UNDERSTANDING QUADRILATERALS questions on Aicharya