I love these hard problems. Oddly enough I think they're fun. Is there anywhere else I could find similar problems?

hey all.

regarding the "right triangle ABC" problem
(found here: http://www.beatthegmat.com/problem-solving-for-780-aspirants-t30325.html)

the solutions above would be nice in a geometry course; a lot of them are very pretty.

but - let's assume that this is a gmat problem. (NOTE: this would not conceivably be a gmat problem - it's too obscure/difficult to show up on the test.

if this were a gmat problem:
* it would be multiple choice, with five NUMBERS as answers - say, 30, 35, 40, 45, 50.
therefore:
* that NUMBER would be the same, regardless of the particular shape of the right triangle ABC.
therefore:
* if you can answer the problem for ANY SINGLE EXAMPLE of ABC, then you've got THE answer.

so:

we can just let ABC be a 45-45-90 triangle.
if that's the case, then BO will be a horizontal line, and it will be clear (from symmetry) that BO cuts right angle ABC into two 45-degree angles.
that's all you need.

again, BECAUSE THE PROBLEM WOULD BE MULTIPLE-CHOICE, there's no need to produce such elaborate general solutions; finding just one solution is sufficient.

Note, however, that you could not use this approach on a question like Q179 in the Problem Solving section of OG12; there one of the answers is 'cannot be determined', which means that it is at least possible that the answer may be different depending on what numbers you start with