a chord of a circle divides the circle into two parts such that the squares inscribed in the two parts have the areas 16 and 144 square units. The radius of the circle, is?

I stole most of this from the web.

From Pythagoras:

AE^2 + DE^2 = r^2

r^2 = (x+4)^2 ..............................(1)

r^2 = (12-x)^2+36

therefore

(x+4)^2 = (12-x)^2+36

simplify and calculate

x= 5

therefore

r = sqrt(9^2 + 4)        (from (1))

= sqrt(85)

Cool solution huh?