Not A Completely Horrendously Easy Geometry Problem
Level
pending
In a certain triangle ABC, the altitude AD, the median BE, and the angle bisector CF are concurrent. Given that AE/EC = f (AF/FB), find |f(i)|.
The answer is 1.
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1 solution
Use ceva's theorem to deduce that f(x)=1/x. Setting 1/i = a+bi, solving by matching coefficients and logic, we have f(i)=-i.The magnitude of -i = 1.