Awesome geometry - 10

Geometry Level 5

Consider a circle with center\( A\).

Consider point \(C\) outside the circle .

Let Point \(B\) be on the circle such that \(\overline{CB}\) is tangent to the circle.

Consider a line passing through Point \(C\) , which intersects the circle at points \(D, F\).

Let \(\overline{BE}\perp \overline{CF}\)

If \(\overline{BD}= 12 , \overline{CD}= 18\),

Find \(\overline{DF} - 2 \times \overline{DE}\)

This problem is a part of set Awesome ' NIHARIAN' geometry.

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