Four points

Geometry Level 3

The \(D, E, F\) points divide the \(AB, BC, AC\) sides to two equal parts, as is shown on the figure below.

The \(T\) point is on \(AB\) line, such that \(TC\) is an altitude of \(\triangle ABC\).

True or False?

There always exist a circle, which goes through all of the \(D, E, F, T\) points.

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