2 tan 2x + tan x = 2 (MD/AD) + (KD/AD) = CD/AD = tan 3x.
However, the addition formula for tangent gives us
tan 2x = (tan 3x - tan x)/(1 + tan x tan 3x)
and substituting this in the last equation tells us that either tan x = tan 3x or tan x tan 3x = 1, i.e., either tan x = tan 3x or tan 3x = tan (pi/2 - x). Since x is between 0 and pi/4 exclusive, the first alternative is impossible and the second implies that 4x = pi/2, so BAC is right, as desired.
David Moews ( email@example.com )
To the puzzle; to the puzzles list; to the home page