▱ in ABCD, e is the midpoint of AB, f is on ad, AF: ad = 1:3, EF intersects AC with G. if AC = 20, then AG=______ ．

Let the midpoint of AC be o, connect EO, and E be the midpoint of AB, ∥ EO ∥ BC, EO = 12bc, ad ∥ BC, ∥ AF ∥ EO, ∥ AFG ∥ OEG, ∥ aggo = afeo. ∵ AC = 20, o be the midpoint, ∥ OA = 10, then go = 10-ag ∵ AF: ad = 1:3, ad = BC, ∥ aggo = afeo = 11.5, ∥ ag10-ag = 11.5

AC is the diagonal of parallelogram ABCD, point E is on ad, AE = 2DE, point F is the midpoint of AB, connecting EF angle AC to point m, if AC = 14, then am =?

Take the midpoint o of AC and connect of, then OA = 1 / 2Ac = 7,
∵ f is the midpoint of AB, ∵ of = 1 / 2BC, of ∥ BC,
ABCD is a parallelogram,
∴AD∥BC,BC=AD,
∴OF∥AD,OF=1/2AD,
∴ΔMOF∽ΔMAE,AE=2/3AD,
∴AM/OM=AE/OF=(2/3)/(1/2)=4/3,
∴AM=4/7OA=4.

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