for some reason i didn't see the (r-140)^2 + (r-70)^2 = r^2 method, i used a much nastier method using trigonometry, but still got the same answer
i considered the triangle of the top left corner of the box, the center of the pizza, and the point where the card meets the pizza.
the edge connecting the corner of the box and the point where the card meets the pizza makes angle arctan(2) with the left side of the box, the edge from the corner of the box to the center of the pizza makes angle 45° with the edge of the box. So the angle in the triangle between these two edges is arctan(2)-45°. Then applying the cosine rule we get:
r^2 = 2r^2 + 24500 - 2(r sqrt(2))(70 sqrt(5))cos(arctan(2) - 45°)
we can show that cos(arctan(2)-45°) = 3sqrt(10)/10, and simplifing the above quadratic gives:
r^2 - 420r + 24500 = 0
(r-70)(r-350) = 0
obviously r = 70 is incorrect...
bit of the long way around
