Blue circle puZZle

Let the radius of the blue circle is $r$ . The power from the center of the blue circle to the big circle is: $(1+r)(5+r)=(2+r)(3+r) \\ r^2+6r+5=r^2+5r+6 \\ r=1$

Let r be the radius of blue circle.
(2r + 6) * (2r + 5) = sqrt{[(r + 2)² + (r + 5)²] * [(r + 1)² + (r + 3)²]} + sqrt{[(r + 2)² + (r + 1)²] * [(r + 5)² + (r + 3)²]}.
Doing all the required expansion, in the end it becomes.
0 = 2r³ + 9r² + 4r - 15.
We get
r = -3 or r = -2.5 or r = 1