Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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The thing I dislike about those kinds of ideas are that they can be tough to get. It does come down to luck and experience a lot.
I do not have an exact definition. Roughly, it means that some times you will think of it, sometimes you won't, and it mostly depends on luck, not unlike many other geometry problems.
Well, I have a solution that takes 2 or 3 lines to write up, but requires quite a bit of inspection.
There's no right angle to get tanA easily so I used the sine and cosine rules:
Put these together to get tanA and simplify.
work on this expression for tanA, making use of the following:
After much simplification you can get this equal to -2tanB, from which the required result follows.
It's a tough one so expect it to take 2 or 3 pages. If you get stuck post back where you've got to, and I'll compare your answer with mine.
if the median 'AD' of a triangle 'ABC' is perpendicular to side AB then prove that 'tanA+2tanB=0'