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Question: Something geometric

Question:Something geometric

Alfred_F 345 Maple
geometry
2 hours ago
0

In the plane, the concentric circles k1 and k2 are given with center M. Circle k1 is the unit circle (radius = 1), and k2 has twice the area of ​​k1. From the outside, five congruent circles k3 are placed tangent to k1, each with a radius r yet to be calculated. Prove that the circles k3 can be arranged such that any two adjacent circles k3 and k2 can have a common intersection point, and these intersection points form the vertices of a regular pentagon. The radius r is to be calculated exactly (no approximation) as a term.
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