1983 AHSME Problems/Problem 29
Revision as of 11:05, 7 June 2016 by Wiggle Wam (talk | contribs) (Created page with "Place the square on the coordinate plane with <math>A</math> as the origin. (This means that <math>B=(1,0), C=(1,1),</math> and <math>D=(0,1).</math>We are given that <math>PA...")
Place the square on the coordinate plane with 
as the origin. (This means that 
and 
We are given that 
so
\begin{align*}&(x^2+y^2)+((x-1)^2+y^2)=(x-1)^2+(y-1)^2\\ &2x^2+2y^2-2x+1=x^2+y^2-2x-2y+2\\ &x^2+y^2=-2y+1\\ &x^2+y^2+2y-1=0\\ &x^2+(y+1)^2=2\end{align*}
Thus, we see that 
is on a circle centered at 
with radius 
The farthest point from 
on this circle is at the bottom of the circle, at 
so 
is 
