Yes, yes, and yes!
The one being cheated on has the right to make an informed decision about their relationship with full disclosure. Avoiding telling them in order to "spare them" or "spare the relationship" are little more than contrived excuses cowards have used to rationalize saving their skin.
It'll hurt, yes, but honesty is what matters, and down the road the one being cheated on will likely find out, only way to keep a secret is if only one person knows.