2010 AMC 12B Problems/Problem 13
Problem
In , and . What is ?
Solution
We note that and . Therefore, the only way to satisfy this equation is if both and , since if either one of these is less than 1, the other one would have to be greater than 1, which contradicts our previous statement. From this we can easily conclude that and and solving this system gives us and . It is obvious that is a triangle and solving for the sides gives us