In the figure shown below, the blue line is 8 units long and the red line is 12 units long. Find the area of the square in square units.
In the small circle we can use the intercepting chords theorem
S = side of square
(S/2 - 8)^2 = (S/2 - 12) (S/2)
S^2 / 4 - 8S + 64 = S^2/4 - 6S
64 = 2S
S = 32
Area =S^2 = 1024
