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How to catch a goat
Bring some grain.
Find the goat by checking hedges for hole, looking up in trees (yes, trees! ), flower gardens, inside your house, down the road, over the river, etc. Goats naturally explore and can be very curious.
Approach slowly from an angle where the goat can see you and the grain bucket. Goats know where their escape routes are, and they are faster and more agile than you, so you don't want to startle it.