四边形ABCD各边相等,∠ABC=60°,直线L过点D,且与BA的延长线和BC的延长线分别交于E,F,M是CE与AF的交

∵AB＝AC＝BC＝AD,∴ABCD是菱形,∴AD∥BF.
∵ABCD是菱形,又∠ABC＝60°,∴△ABC、△ACD都是正三角形,
∴AC＝AB＝BC、∠BAC＝∠ACB＝60°,∴∠EAC＝∠ACF＝150°.
∵AD∥BF,∴△EAD∽△EBF,∴EA/EB＝AD/BF,∴EA/（EA＋AB）＝AD/（BC＋CF）,
又AC＝AB＝BC,∴EA/（EA＋AC）＝AC/（AC＋CF）,∴由分比定理,有：EA/AC＝AC/CF.
∵∠EAC＝∠ACF、EA/AC＝AC/CF,∴△EAC∽△ACF,∴∠AEC＝∠MAC.
∵∠AEC＝∠MAC、∠ACE＝∠MCA,∴△ACE∽△MCA,∴CA/CM＝CE/CA,
∴CA^2＝CM×CE.