2021 AMC 10B Problems/Problem 23
Problem
A square with side length 
is colored white except for 
black isosceles right triangular regions with legs of length 
in each corner of the square and a black diamond with side length 
in the center of the square, as shown in the diagram. A circular coin with diameter 
is dropped onto the square and lands in a random location where the coin is completely contained within the square. The probability that the coin will cover part of the black region of the square can be written as 
[asy]
/* Made by samrocksnature */
draw((0,0)--(8,0)--(8,8)--(0,8)--(0,0));
fill((2,0)--(0,2)--(0,0)--cycle, black);
fill((6,0)--(8,0)--(8,2)--cycle, black);
fill((8,6)--(8,8)--(6,8)--cycle, black);
fill((0,6)--(2,8)--(0,8)--cycle, black);
fill((4,6)--(2,4)--(4,2)--(6,4)--cycle, black);
filldraw(circle((2.6,3.31),0.47),gray);
[/asy]
