2009 AMC 12 B Problem 16 (Angle Bisector Theorem, Trapezoid)

[@defunct6613]

I actually found another method which simply used triangle similarity (Check this out; this is really cool): Extend CD and BA to meet at E. Then angle BED = 180 - (23 + (180 - 46) ) = 23 (degrees). Therefore BED is an isosceles triangle. The implication is DE = BD = 1. Now observe that triangle AED is similar to triangle BEC, from which it follows that CE/DE = 9/5, which means CD = 4/5.

[@particleonazock2246]

Underrated, but where is your video on the angle bisector theorem that you mentioned you were going to put as the i.