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UKMT Intermediate Mathematical Challenge, 2022

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The first figure shows four touching circles of radius 1 cm in a horizontal row, held together tightly by an outer band X. The second figure shows six touching circles of radius 1 cm, again held tightly together by a surrounding band Y. Which of the following statements is true?

(A) X is 2 cm longer than Y (B) X is 1 cm longer than Y (C) X and Y are the same length (D) Y is 1 cm longer than X (E) Y is 2 cm longer than X

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