The lengths of the sides of a convex hexagon
![ABCDEF](/media/m/9/f/e/9fe205b534135e3a700ffb54d8b96cb0.png)
satisfy
![AB = BC](/media/m/b/2/a/b2a105eba9f5fa3153680feda9fdd441.png)
,
![CD = DE](/media/m/e/8/9/e89b0b98d7a4db33daf10c4634c643e1.png)
,
![EF = FA](/media/m/0/9/4/09444361040c24d6a2fb9f853619b0be.png)
. Prove that:
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The lengths of the sides of a convex hexagon $ABCDEF$ satisfy $AB = BC$, $CD = DE$, $EF = FA$. Prove that:
$$\frac {BC}{BE} + \frac {DE}{DA} + \frac {FA}{FC} \geq \frac {3}{2}.$$