From Longman Dictionary of Contemporary Englishsquare the circlesquare the circleIMPOSSIBLEto attempt something impossible → square
Examples from the Corpus
square the circle• On his last point, Labour has manifestly failed to square the circle.• Britain, ever the Atlanticist, tried to square the circle, and usually failed.• The only way of squaring the circle to Moscow's satisfaction would be to send in troops. 