As shown in the figure, the side length of equilateral triangle ABC is 6, ad is the middle line on the side of BC, M is the moving point on ad, e is the point on AC, if AE = 2, then the minimum value of EM + cm is?

Let e be a symmetric point F with respect to ad, then f is on AB, connecting FC with AD and m, and then the point m is the desired point
The minimum value of EM + cm is FM + MC = FC. According to the cosine theorem, for any triangle, the square of any side is equal to the sum of the squares of the other sides minus the cosine of the angle between the two sides and them. If the three sides are a, B, C and the triangle is a, B, C, then it satisfies the property a ^ 2 = B ^ 2 + C ^ 2 - 2 · B · C · cosa
The square of FC is AF square plus AC square minus 2AF times accosa = 4 + 36-2 * 2 * 6 * 1 / 2 = 28
So the minimum value is 2 times the root 7

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