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Gov. John Kasich was the winner in the Republican primary in his home state, Ohio, on Tuesday, according to The Associated Press, dealing a setback to Donald J. Trump and keeping his presidential hopes alive.

The victory is the first for Mr. Kasich in a primary election or a caucus this year. The Republican governor, who faces a steep delegate deficit against his rivals, has predicted that a win in Ohio would reset the race.

Mr. Trump campaigned aggressively in Ohio in hopes of clearing Mr. Kasich from the field. That is now unlikely to happen anytime soon.

There were 66 delegates at stake in Ohio, which awards them on a winner-take-all basis for Republicans.

On CNN, Mr. Kasich said he wanted to “bring the country together and not divide this country anymore.”

“That’s why this was such a big victory tonight,” he said. “Because what it does is it says, ‘You want to go and divide ’em?’ O.K., you came to Ohio, you threw everything you had at me, and guess what? It didn’t work.”