Consider a circle with center O. As shown in the figure, we draw chord CD and an additional circle centered at Q, tangent to CD at point T, and intersecting the original circle at A and B. The extensions of lines AC and BD meet at H. Likewise, extensions of lines AT and BT intersect BH and AH at E and F. Given CF = 2, FH = 6, and EH = 4 units, find the length of DE.

In circle's embrace,

Chord and tangent interlace,

Figures intertwine,

Lines converge in graceful dance,

DE's length we seek, advance.

In this illustration, stereographic projection and mathematical
transformations are utilized to distort and reshape the geometry figure of
problem 1554, producing distinctive spherical effects. This exemplifies an
engaging application of geometry in digital image editing, empowering users to
create visually captivating images from their figures.

Stereographic projection is a mathematical technique that maps points on a sphere to points on a plane (flat surface).

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