# Marion's Theorem

Let

*ABC*be any triangle. Trisect each side, so that

*AB*has

*C*

_{1}and

*C*

_{2}as the two trisection points and similarly for the other two sides. Draw the lines

*AA*

_{1},

*AA*

_{2},

*BB*

_{1},

*BB*

_{2},

*CC*

_{1},

*CC*

_{2}. These lines define an hexagonal region in the middle of triangle

*ABC*. Then the area of the hexagonal region is

^{1}/

_{10}the area of

*ABC*.