In triangle ABC, ad is the middle line, AE is the middle line of triangle abd, and angle bad = angle BDA

Take the midpoint F of AC and connect DF, then DF is the median line, so DF is parallel to AB and equal to half of ab
Because angle bad = angle BDA, DB = ab
So DF = half of DB = EB
Because DF is parallel to AB, angle CDF = angle EBA
And because CD = dB, so CD = AB, so the triangle CDF is all equal to the triangle Abe
So AE = CF = half of AC
So AC = 2ae

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