Wasn't it easy to find an equilateral triangle's side

Geometry Level 4

ABCABC is an equilateral triangle. DEDE is the tangent to the inscribed circle with DD on ABAB and EE on ACAC. It is given that DEDE perpendicular to ACAC and AE=10AE=10.The side length of ABCABC can be expressed as a+bca+b\sqrt{c} where aa and bb are positive integers and cc is square-free positive integer; then find a+b+ca+b+c.

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