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| − | <asy>
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| − | unitsize(12);
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| − | pair A,B,C,X,Y,Z;
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| − | A = (0,0); B = (60/7,24*sqrt(6)/7); C = (21,0);
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| − | X = (20/7,8*sqrt(6)/7); Y = (387/35,96*sqrt(6)/35); Z = (147/8,0);
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| − | draw(A--B--C--cycle);
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| − | dot(A); dot(B); dot(C); dot(X); dot(Y); dot(Z);
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| − | draw(X--(118/7,8*sqrt(6)/7));
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| − | draw(Y--(21/5,0));
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| − | draw(Z--(15/2,3*sqrt(6)));
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| − | label("$\frac{21}{5}$",(21/10,0),S);
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| − | label("$\frac{21}{5}$",(347/70,8*sqrt(6)/7),NE);
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| − | label("$\frac{21}{8}$",(315/16,0),S);
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| − | label("$\frac{21}{8}$",(1741/112,8*sqrt(6)/7),NW);
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| − | label("$\frac{287}{40}$",(10,8*sqrt(6)/7),S);
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| − | </asy>
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