### Brain Teasers

# Mystery Circles

Outside the lost city of Xaitec, archaeologists have noticed three rings of large stones, each with a straight line of stones beside it. Twins Sari and Devon have been asked by the chief archaeologist to see whether there may be a connection between the rings and the lines.

The twins decide to determine the diameters of the circles by stretching measuring tape across the widest part of each circle. They find the diameters to be 4.68 m, 9.36 m, and 14.04 m. They measure each of the corresponding straight lines of stones, finding them to be 14.7 m, 29.4 m, and 44.1 m, respectively.

They show the numbers to Jody, who is in charge of mapping. Jody looks at the numbers and says, "Fascinating. Have you seen the connection?" Sari says, "Well, the second circle is twice as wide as the first, and the third is three times as wide as the first." Devon adds, "And the same ratios apply to the straight lines!"

"Fine!" says Jody. "But how is each circle related to the straight line next to it?"

What is the answer to Jody's question?

The twins decide to determine the diameters of the circles by stretching measuring tape across the widest part of each circle. They find the diameters to be 4.68 m, 9.36 m, and 14.04 m. They measure each of the corresponding straight lines of stones, finding them to be 14.7 m, 29.4 m, and 44.1 m, respectively.

They show the numbers to Jody, who is in charge of mapping. Jody looks at the numbers and says, "Fascinating. Have you seen the connection?" Sari says, "Well, the second circle is twice as wide as the first, and the third is three times as wide as the first." Devon adds, "And the same ratios apply to the straight lines!"

"Fine!" says Jody. "But how is each circle related to the straight line next to it?"

What is the answer to Jody's question?

### Hint

Use a calculator to explore the ratios.### Answer

The measure of each straight line represents the circumference of the corresponding circle.If the twins were to divide the measure of each straight line by the diameter of the corresponding circle, they would get a quotient of 3.14 in all three cases. This quantity is the famous number pi, and the circumference of any circle is pi times the diameter. So what Jody noticed was that each straight line represented the circumference of the corresponding circle.

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