just so we're clear on this, pie is something you eat ... pi is the Greek letter that represents the value of the ratio of the circumference of a circle to its diameter.
(a, pi/18) in rectangular coordinates is (a*cos(pi/18), a*sin(pi/18))
(2a, 4pi/18) in rectangular coordinates is (2a*cos(2pi/9), 2a*sin(2pi/9))
using the distance formula for rectangular coordinates ...
16 = [2a*cos(2pi/9) - a*cos(pi/18)]^2 + [2a*sin(2pi/9) - a*sin(pi/18)]^2
16 = 4a^2*cos^2(2pi/9) - 4a^2*cos(2pi/9)cos(pi/18) + a^2*cos^2(pi/18) +
4a^2*sin^2(2pi/9) - 4a^2*sin(2pi/9)sin(pi/18) + a^2*sin^2(pi/18)
16 = 5a^2 - 4a^2[cos(2pi/9)cos(pi/18) + sin(2pi/9)sin(pi/19)]
16 = 5a^2 - 4a^2*cos(2pi/9 - pi/18)
16 = 5a^2 - 4a^2*cos(pi/6)
16 = 5a^2 - 2sqrt(3)*a^2
16 = a^2[5 - 2sqrt(3)]
a = +/- 4/sqrt[5 - 2sqrt(3)]
