A Triangle Evolves Into A Hexagon

Geometry Level 2

Consider an acute angled ΔABC \Delta ABC with circumcircle ω \omega and circumcenter O O . Now, construct points (on the circumcircle) diametrically opposite to the vertices of the triangle, and name them A,B A', B' and C C' as shown in the figure. The area of ΔABC \Delta ABC is 18 18 square units.

Find the area of polygon ABCABC AB'CA'BC' .

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