On a circle of radius R, points K M N are successively marked, which divided the circles
| May 7, 2021 | education
On a circle of radius R, points K M N are successively marked, which divided the circles into arcs KM MN NK in a ratio of 8/7/3. find the lengths of the arcs.
1) The entire circumference is 2πR.
2) Let 8x be the length of the arc KM. Then, since the lengths of the arcs are in the ratio 8: 7: 3, then 7x is the length of the arc MN, 3x is the length of the arc NK.
3) Equate the sum of the arc lengths to the circumference: 8x + 7x + 3x = 2πR, 18x = 2πR, whence x = πR / 9.
4) Then 8πR / 9 is the length of the arc KM, 7πR / 9 is the length of the arc MN and πR / 3 is the length of the arc NK.
ANSWER: 8πR / 9, 7πR / 9 and πR / 3.
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