Mad Angles
Geometry
Level
3
In a triangle ∆ABC, if median AD is perpendicular to the side AB, then find- tanA + 2.tanB
The answer is 0.
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1 solution
Extend BA to F such that CF is perpendicular to BF. You will see that AF=BA, as ∆BFC is similar to ∆ BAD and D is the mid point. Now, tan(π-A) = -tanA = -(CF/AF) And tanB = (CF/BF) = CF/2AF. Thus, tanA + 2.tanB = -(CF/AF) + 2 (CF/2AF) = 0.