UKMT - Grey Kangaroo - 2023 - 9 | Exact Science

9

The diagram shows five equal semicircles and the lengths of some line segments. What is the radius of the semicircles?

A. 12 B. 16 C. 18 D. 22 E. 28

Answer

C

SOLUTIOn

Let the radius of each semicircle be r. From the diagram we can see that 2r +12+2r +12+2r = 22 + 2r + 16 + 2r + 22 and hence 6r + 24 = 4r + 60. Therefore 2r + 24 = 60 and so 2r = 36 and hence r = 18.

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