There were 6 solutions received. Correct solutions were also received from Kevin Bourrillion, Jeff Decker, Mike Fitzpatrick, Michael Lepley.

The equation of the semicircle is y² = R² - (x-R)². The equation of the other circle is y² = r² - x². Solve these simultaneously to get their point of intersection having coordinates (r²/(2R), r(1-r²/(4R²))^(1/2). Find the equation of the line going through that point and (0,r). The point of intersection of that line and the x-axis is -r²/(R(-2+(4-r²/R²))^(1/2)). Take the limit as r goes to 0; it's of the form 0/0 so use L'Hopital's Rule once to get 2R(4-r²/R²)^(1/2) which goes to 4R as r goes 0.

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