I want to place a set of launchers to a series of apps in my application. Is there a way to launch another app from windows phone 7 when an icon is clicked?
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No, there is no way how to launch another app in WP7.
You can use only predefined choosers or launchers, but you cannot launch 3rd party apps:
http://msdn.microsoft.com/en-us/library/windowsphone/develop/ff769550(v=vs.105).aspx
In Windows Phone 8 however you can use so called protocol handlers, so for example if you wan to launch Skype with selected user, you can use something like:
await Windows.System.Launcher.LaunchFileAsync("skype:myskypeid");
This functionality is currently not widely used, so we should see more usage of these launchers in the near future.
These Uri shemes are already working and you can use them:
http://msdn.microsoft.com/en-us/library/windowsphone/develop/jj662937(v=vs.105).aspx
Guide how to use the Uri protocol handlers and file associations in WP8:
http://blogs.microsoft.co.il/blogs/alex_golesh/archive/2012/11/02/what-s-new-in-windows-phone-8-4-out-of-8-protocol-handler-and-file-extensions.aspx