Kef LS50 - can it handle a subwoofer properly?

I just got a pair of KEF LS50 speakers. As is known they are active speakers and I'm considering adding a subwoofer. They have facilities for a sub but what should I do regarding bass management?, they don't have an  amp, so no such feature, and I suspect the sub will just duplicate the lower frequencies from the speakers and I would like the proper function with the highs and mids on the KEFs and the sub  handling only the lower bass. Any solution greatly appreciated. 

You can use an active crossover. That would connect to the KEFs and whatever amp you'll use to drive your subwoofer.
You should download the wireless app for your speakers and see what controls they give you on the sub output. If you have a choice, I'd start with the crossover at 80hz with a 24db/octave slope.

Some subs have parametric EQ (SVS Ultra does) so that you can compensate for room nodes.

The sub will have FAR lower distortion at bass frequencies than your Kefs. At 50hz the distortion of the regular LS50 is only 20db below signal level. Even at 100hz, those little midbass drivers have major distortion.
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Bass management is a HT solution. For music, you should deal with it yourself. If you buy a powered sub it should come with a built in xover, and instructions on how to set it up. There's no reason to make it complicated. People were setting up subs long before there were HT processors with bass management features.
Only thing you need to be aware of is that they won’t play LFE tracks when you attach a subwoofer to the Kefs. They handle a subwoofer fine for music but not for movies. The signal is a 2.0 signal and there’s no proper .1 channel.
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What you need to do this the right way is two subs and a MINI DSP 2x4 total control over the bass and main speakers . 
Would as LS-50 wireless plus a HSU sub (10 inch) be good in a family room with a cathedral ceiling?
Within the limits of the LS-50 it works fine. I ran two Hsu 10 inchers but one is almost as good. 
yes.  no processing or crossovers needed- just a sub with the right connections and adjustments.  KEF LS50- perfectly flat response through the bass region-