I want to describe my hobbies and would like to say that I like bicycles.
- ride as noun: I like ride a bicycle
- ride as verb: I like to ride a bicycle
Which variant is right?
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"I like to ride a bicycle" means the same as "I want to ride a bicycle", so you shouldn't use this variant in your context.
Out of the two presented, only the latter variant is correct, that is:
BUT, an even better variant would be:
When using the form with ride as a noun, we say "I like to ride".
When using ride as a verb, we say "I like riding".
But it doesn't sound right to say "I like to ride a bicycle" with the indefinite article "a". Instead we say:
"I like to ride bicycles", or "I like to ride my bicycle".
Or just avoid it altogether and say: I enjoy cycling!