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HMMT Geometry 2019/6: This is not an olympiad

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February 17, 2019
HMMTgeometry

Problem Statement

Six unit disks C1C_1, C2C_2, C3C_3, C4C_4, C5C_5, C6C_6 are in the plane such that they don't intersect each other and CiC_i is tangent to Ci+1C_{i+1} for 1≤i≤61 \le i \le 6 (where C7=C1C_7 = C_1). Let CC be the smallest circle that contains all six disks. Let rr be the smallest possible radius of CC, and RR the largest possible radius. Find R−rR - r.
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