I have this question I can't seem to find a solution to:
$\triangle$ABC is a triangle such that AD is the altitude from A to BC, BE is the altitude from B to AC and CF is the altitude from C to AB.
Now complete $\triangle$DEF.
Find the ratio of Area $\triangle$DEF to Area $\triangle$ABC.
I think it has to something to do with the incenter- excenter lemma( Although I couldn't solve it that way). I tried using the sine rule and the fact that the line OD, OE and OF bisect the interior angles of $\triangle$DEF. And I'm stuck.
The answer is in terms of $\sin$ and cos of the angles A, B, C according to the answer key.
Any and all help is appreciated!
Thanks in advance.