1987 AMC 12 #21 - Square Inscribed in Triangle
Source:
January 1, 2012
geometryAMC
Problem Statement
There are two natural ways to inscribe a square in a given isosceles right triangle. If it is done as in Figure 1 below, then one finds that the area of the square is . What is the area (in ) of the square inscribed in the same as shown in Figure 2 below?
[asy]
draw((0,0)--(10,0)--(0,10)--cycle);
draw((-25,0)--(-15,0)--(-25,10)--cycle);
draw((-20,0)--(-20,5)--(-25,5));
draw((6.5,3.25)--(3.25,0)--(0,3.25)--(3.25,6.5));
label("A", (-25,10), W);
label("B", (-25,0), W);
label("C", (-15,0), E);
label("Figure 1", (-20, -5));
label("Figure 2", (5, -5));
label("A", (0,10), W);
label("B", (0,0), W);
label("C", (10,0), E);
[/asy]