Question

A circle is drawn through the vertices of a square with sides of 5 inches. If a dart is thrown at random into the circle, what is the probability it will NOT lie in the square. Use pythagoreean theorem to find the radius of the circle.

Answer 1

R= Radius = (1/2) of diagonal of square = (1/2)[ 5^2 + 5^2 ]] ^ (1/2) = sqrt(50)/2
P (not in square) = (Area circle - Area square) / Area circle
= (pi*R^2 - 25)/(pi*R^2)
= (pi*(sqrt(50)/2)^2 - 25)/(pi*(sqrt(50)/2)^2)
= (pi*(50/4) - 25)/(pi*50/4)
=25*(2*pi/4 - 1)/((2*pi/4)*25)
= (pi/2 - 1)/(pi/2)
= 1 - 1/(pi/2)
= 1 - 2/pi