Difference between revisions of "2017 AMC 8 Problems/Problem 25"
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==Solution 1== | ==Solution 1== | ||
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<asy>draw((1,1.732)--(2,3.464)--(3,1.732)); draw(arc((0,0),(2,0),(1,1.732))); draw(arc((4,0),(3,1.732),(2,0))); label("$U$", (2,3.464), N); label("$S$", (1,1.732), W); label("$T$", (3,1.732), E); label("$R$", (2,0), S);</asy> | <asy>draw((1,1.732)--(2,3.464)--(3,1.732)); draw(arc((0,0),(2,0),(1,1.732))); draw(arc((4,0),(3,1.732),(2,0))); label("$U$", (2,3.464), N); label("$S$", (1,1.732), W); label("$T$", (3,1.732), E); label("$R$", (2,0), S);</asy> | ||
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==Video Solutions== | ==Video Solutions== | ||
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https://youtu.be/sVclz6EmpEU | https://youtu.be/sVclz6EmpEU | ||
~savannahsolver | ~savannahsolver | ||
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Latest revision as of 22:44, 18 October 2024
Problem
In the figure shown, and are line segments each of length 2, and . Arcs and are each one-sixth of a circle with radius 2. What is the area of the region shown?
Solution 1
In addition to the given diagram, we can draw lines and The area of rhombus is half the product of its diagonals, which is . However, we have to subtract off the circular segments. The area of those can be found by computing the area of the circle with radius 2, multiplying it by , then finally subtracting the area of an equilateral triangle with a side length 2 from the sector. The sum of the areas of the circular segments is The area of rhombus minus the circular segments is
~PEKKA
Video Solutions
~savannahsolver