Where Are They Concurrent?

Geometry Level 5

Let $$\triangle ABC$$ be an acute triangle, and let $$D,E,F$$ be the midpoints of $$BC,CA,AB$$ respectively. Let $$A', B', C'$$ be the diametrically opposite points of $$A,B,C$$ respectively on the circumcircle of $$\triangle ABC.$$ It turns out that lines $$A'D, B'E, C'F$$ are concurrent at a point $$X$$ within $$\triangle ABC.$$ Then, $$X$$ is the ...... of $$\triangle ABC.$$

Details and assumptions

• The diametrically opposite point of a point $$P$$ on a circle $$\omega$$ is the unique point $$P'$$ also lying on $$\omega$$ apart from $$P$$ such that $$PP'$$ is a diameter of $$\omega.$$
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