2005 AMC 12B Problems/Problem 18
Problem
Let 
and 
be points in the plane. Define 
as the region in the first quadrant consisting of those points 
such that 
is an acute triangle. What is the closest integer to the area of the region ?
Solution
For angle 
and 
to be acute, must be between the two lines that are perpendicular to $\overbar{AB}$ (Error compiling LaTeX. Unknown error_msg) and contain points and . For angle to be acute, first draw a 
triangle with 
as the hypotenuse. Note cannot be inside this triangle's circumscribed circle or else
