Say you have a right triangle, you know the length of the 2 sides of the 90 degree corner (so you know everything, the hypotenuse and all 3 angles). Inside this triangle, you draw a line (not the height) so you create 2 new (non-similar) triangles: 1 new right triangle and another one.
Is there something that the original big right triangle (ABD) and the new smaller triangle (ABC) have in common? I am looking for a ratio that stays constant, using some property of both triangles: angles, surface, circumference, inside circle ratio, height,... I.e. the ratio of some function of alpha / (AC/AE) = that function of beta / (AD/AF), something like that, or BC/BD= ...* some function (alpha/Beta), or ... I've looked at http://en.wikipedia.org/wiki/Right_triangle, but it's not clear to me. Thanks for the help!