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File:AMC12 2006A 17.png pair A=(0,3), B=(0,0), C=(3,0), D=(3,3), E=(3+5/3/sqrt(2),3+5/3/sqrt(2)), F; ...9+5*sqrt(2))*expi(atan(5/(3*sqrt(2))/(3+(5/3/sqrt(2))))+atan(5/(3*sqrt(9+5*sqrt(2)))));(232 × 236 (5 KB)) - 19:11, 8 November 2007
File:AIME 2005I Solution 7 1.png ...+sqrt(141),4*sqrt(3)), D=(5,5*sqrt(3)), E=(5,0), F=(5+sqrt(141),0), G=(5,4*sqrt(3)); label("A",A,(-1,-1));label("B",B,(1,-1));label("C",C,(1,1));label("D",D,(-1,1));(234 × 112 (4 KB)) - 21:26, 9 November 2007
File:AIME 2005I Solution 7 2.png ...+sqrt(141),4*sqrt(3)), D=(5,5*sqrt(3)), E=((9+sqrt(141))/2,(9+sqrt(141))/2*sqrt(3)); label("A",A,(-1,-1));label("B",B,(1,-1));label("C",C,(1,1));label("D",D,(-1,1));(234 × 204 (5 KB)) - 21:46, 9 November 2007
File:AIME 2005II Solution 12 1.png pair A=(0,9), B=(9,9), C=(9,0), D=(0,0), E=(2.5-0.5*sqrt(7),9), F=(6.5-0.5*sqrt(7),9), G=(4.5,9), O=(4.5,4.5); label("A",A,(-1,1));label("B",B,(1,1));label("C",C,(1,-1));label("D",D,(-1,-1));(234 × 233 (4 KB)) - 22:02, 9 November 2007
File:17IMG 20221113 140112.jpg Using the AM-GM inequality, q+r/2 = sqrt(qr) if and only if q = r, which is shown.(1,254 × 1,672 (139 KB)) - 10:04, 13 November 2022
