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UKMT Senior Kangaroo, 2019

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Identical regular pentagons are arranged in a ring. The partially completed ring is shown in the diagram. Each of the regular pentagons has a perimeter of $65$ . The regular polygon formed as the inner boundary of the ring has a perimeter of $P$ . What is the value of $P$ ?

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