mathgeometry
posted by paragon .
The sum of the radii of two concentric circles is 40. A chord with length 36 of the larger circle is trisected by the smaller circle. The area of the smaller circle is k*pi. Find the value of k. Express your answer as an exact decimal.
Please show work. Thank you very much.

r + R = 40
so
r = 40  R
pi r^2 = k pi
so
k = r^2
right triangles from center to middle of chord
r^2  6^2 = R^2  18^2
R^2 r^2 = 32436 = 288
so we have two equations
R = 40  r
R^2 r^2 = 288
then
(40r)^2 r^2 = 288
1600 80 r +r^2r^2 = 288
80 r = 1312
r = 16.4
r^2 = 268.96
but k = r^2 = 268.96