Three circles are enclosed in a rectangle such that each circle is tangent with one another and the rectangle.
The dimensions of the rectangle are \((8\sqrt6+20)\) by 24.
A triangle is formed using the points of tangency of the circles as vertices.

Find the area of the triangle, which can be expressed as the expression \(\frac{a\sqrt{b}}{c}\) in lowest terms, where \(a\), \(b\) and \(c\) are integers. Submit your answer as \(a+b+c\).

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