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Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1178.
Lets assume AD extended meets circumcircle of Tr.ABC at point E. Assuming DE=x, we have d.x= BD.CD BD = ac/(b+c), CD = ab/(b+c) Also Tr. ACD is similar to Tr.AEB We have d/c=b/(d+x) we get d^2 = bc - dx or d^2 = bc - BD.CDSubstituting values of BD and CD we get required expression.
Perhaps the easiest way of doing this thro' pure geometry alone