Finding the Shaded Area + Proof that Medians are Concurrent (Solution 79)

We prove three elementary yet beautiful theorems of medians and the centroid of a triangle, which results in a trivial solution of the initially complicated-looking problem.

Congratulations to Walt S, Minh Cong Nguyen, Theodore Leebrant, Varun Shah, Zemlya Drakona, Fernando Peñaherrera, Alex Burns, Fysty, Serengeti Ghasa, and fabio alan for successfully solving this challenge question! Walt S was the first person to solve the question.

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[zmaj]

Wait. Is the fact that point I is the incenter irrelevant?

EDIT: It is, I confirmed in GeoGebra. In fact, the point I can even be outside the triangle. However, it is possible to get the hexagon to intersect itself if the order that the points are connected remains the same.

[prabhatkusahu]

[DEF]=1/4 ∆=1/8
[JKL]=1/9∆=1/18
[AJBKCL]=2/3∆=1/3
With love and regards
Prabhat Kumar Sahu
Singhijuba Sonepur
Odisha India
Can I get bonus prize