The tiddlywiki way is to have the radio buttons set a value into a field and then display the corresponding card based on the field being populated
Pseudo code:
<$radio tiddler=<<currentTiddler>> field="card-state" value="Card-1">Card 1 </$radio>
<$radio tiddler=<<currentTiddler>> field="card-state" value="Card-2">Card 2 </$radio>
<$radio tiddler=<<currentTiddler>> field="card-state" value="Card-3">Card 3 </$radio>
<$reveal type="match" state="!!card-state" value="Card-1">
Card 1 content
</$reveal>
<$reveal type="match" state="!!card-state" value="Card-2">
Card 2 content
</$reveal>
<$reveal type="match" state="!!card-state" value="Card-3">
Card 3 content
</$reveal>