ABC is a sector of a circle with radius R and center C. The arc DE lies on a circle also centred at C. If DE divides ABC into two regions of equal area, find the length of CD in terms of R

Answer 1

If we call DE r, then we have

r^2θ = 1/2 R^2θ
r^2 = R^2/2
r = R/√2

or, since the areas are in the ratio 1:2, the radii are in the ratio 1:√2