You could improve usability by employing ‘submit’ elements instead of all radiobuttons, and offloading the ‘new tab’ functionality to a hotkey: that way, you'd tab-and-enter to fire one of the non-default searches, or Ctrl-enter for a new tab (or Cmd-enter on Mac; though I'm not sure why you'd want to open a new tab from the start page). The hotkey here would have to be implemented with JS.
But, in case you're using Firefox, you have an even better option of putting those search options into search keywords such that “ddgv something” would get you to the video search straight from the address bar.
In Chrome, IIRC you can do a similar thing by assigning a keyword which would work with “keyword”-tab-searchphrase, but a) I don't remember how it's done, and b) Chrome's address bar doesn't seem to rank searches as domain visits, so a partial keyword entry tends to be replaced with another domain, which is annoying.
But, in case you're using Firefox, you have an even better option of putting those search options into search keywords such that “ddgv something” would get you to the video search straight from the address bar.
In Chrome, IIRC you can do a similar thing by assigning a keyword which would work with “keyword”-tab-searchphrase, but a) I don't remember how it's done, and b) Chrome's address bar doesn't seem to rank searches as domain visits, so a partial keyword entry tends to be replaced with another domain, which is annoying.