The circumference of a circle circumscribing an equilateral triangle is units. Find the number of square units in the area of the circle inscribed in the same triangle.
Source: NCTM Mathematics Teacher, February 2006
In equilateral triangle , angle bisector is also the perpendicular bisector of . That makes point I the circumcenter, the incenter, and the centroid of triangle .
because is the centroid
Area of incircle
Answer: square units