Joseph Farah, a 61-year-old author, had long labored on the fringes of political life, publishing a six-part series claiming that soybeans caused homosexuality and fretting that “cultural Marxists” were plotting to destroy the country.

But in early 2011, he received the first of several calls from a Manhattan real estate developer who wanted to take one of his theories mainstream.

That developer, Donald J. Trump, told Mr. Farah that he shared his suspicion that President Obama might have been born outside the United States and that he was looking for a way to prove it.

“What can we do to get to the bottom of this?” Mr. Trump asked him. “What can we do to turn the tide?”

Mr. Farah recalled that Mr. Trump even proposed dispatching private investigators to Hawaii, Mr. Obama’s birthplace, to resolve the debate.

More: Inside the Six Weeks Donald Trump Was a Nonstop ‘Birther’