Wir haben zu Hause eine Geige, dabei kann keiner in meiner Familie Geige spielen.
That's the most common way to phrase it. That is because Geige spielen is a verb phrase as Rad fahren. It's not about a particular violine but about the ability to play violine.
BUT you could also say
Wir haben zu Hause eine Geige, dabei kann keiner in meiner Familie die Geige spielen.
This is not super common but also not about that particular violine. The verb phrase die Geige spielen a more refined way to say Geige spielen. It is often phrased that way when it is about playing musical instruments.
On the other hand, no one says das Rad fahren when they don't mean a particular bicycle.
This is again one of those questions native speakers would get "wrong". Your materials are confusing.