Circle tangent triangle perimeter

Geometry Level 3

Points \(A\) and \(B\) lie on a circle \(\Gamma\) with radius 123, such that their tangents intersect at \(C\) and satisfy \( \angle ACB = 90^\circ \). \(D\) is a point chosen on minor arc \( AB\) of circle \(\Gamma\). The tangent at \(D\) intersect \(AC\) and \(BC\) at \(E\) and \(F\) respectively. What is the perimeter of triangle \(CEF\)?

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