I have another one I need help I cantt remember all my trian

I have another one I need help I cant\'t remember all my triangle rules it has been a while. I was able to label the diagram with the colored lines. just need help solving it now.

Thanks,

Solution

If we look at the triangle formed by the pink line , blue line and green line is

a right angled triangle.

hypotenuse = radius of circle = r

length of blue line = r - 1.74

Apply right anged triangle property:

r^2 = (2.385)^2 + (r -1.74)^2

r^2 = 8.715 + r^2 - 3.48r

3.48r = 8.715

r = 2,5 cm

Radius of circle = 2.5 cm