The following figure has two axes of symmetry which define its width and length. The length (horizontal distance) is twice the width (vertical distance). The largest circle has a radius of 2005 and all the contacts with small circles are tangent. If the six smallest circles have the same radii, then what’s the radius of the medium circle? Swiss competition: https://fsjm.ethz.ch/static/oldwebsite/documents/FI_19e_1.pdf
y:distance between the center of the medium circle and the large circle
x:distance between the center of the large circle and the small circle
r:the radius of the small circle
I then drew two 30,60,90 triangles and set up a system of equations:
And I didn’t get the right answer.