2007 Alabama ARML TST Problems/Problem 2
The points and lie in that order on a line. Point lies in a plane with and such that . Given that , , and , compute the number of positive integer values that can take on.
is external to at . Therefore it is equal to the sum:
Then, according to the problem statement:
As y cancels, its value is not bounded by this algebraic relation.
However we note that by the problem statement cannot be greater than .
The two angles sum to , thus
Noting that , it becomes clear that