例1如图1,在边长为2的菱形ABCD中,∠A=60°,M是AD的中点,N是AB边上的动点,将△AMN沿MN所在直线翻折到△A′MN,连接A′C,求线段A′C的最小值.解以M为圆心,MD为半径作圆,连接MC,与圆的交点即为所求A′点.因为MA′+A′C≥MC,又因为MA′,MC是定值,当且仅当A′C取最小值时等号成立.所以,A′C的最小值为MC-MA′. Example 1 As shown in Figure 1, in a diamond ABCD with a side length of 2, ∠A = 60 °, M is the midpoint of AD, N is the moving point on the AB side, and Δ AMN folds along the line where MN is to ΔA ’MN, connect A’C, Find the minimum value of the segment A’C. Solution to M as the center, MD for the radius of a circle, connecting the MC, the intersection of the circle is the required point of A. Because MA’ + A ’ C≥MC, and because MA ’, MC is a fixed value, if and only if A’C take the minimum value equal to, so A’C the minimum value of MC-MA’.