Do you finesse or play high?

We are looking at situations in which third hand should or should not follow the "third-hand high" mantra. Which is right here? South is in four hearts. West leads a fourth-highest diamond two. After dummy plays low, should East put in his nine or rise with the king?

North knew that his hand was a tad strong for a four-heart "weak freak" raise, but he knew that it was unlikely his side had a slam, and he was worried that the opponents might be able to do well in spades.

East should work out who has what in diamonds. He knows that South has the ace, because West would not have led a diamond away from the ace. And South presumably has three diamonds. West probably has the queen, and might have the 10 as well. (If West had started with 10-high diamonds, he likely would have led from a stronger suit.)