Difference between revisions of "2019 AMC 10B Problems/Problem 20"
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| − | The answer is 14. First, find the area of the semicircle by squaring the radius of the larger circle, multiplying it by pi, and dividing by 2. to find the grey parts in between the semi-circles, create a shape using two-quarter circles with radius's of 1 on the outside, and a rectangle with sides 2 and 1. Find the area, then subtract that area by two semicircles with a radius of 1. The difference would give you the grey area, then multiply the difference by two since there are two of them. Next, construct a 30, 60, 90 triangle using a line drawn from point F, intersecting the circle with a radius of 2 and a semicircle with radius 1 (it could be either the right or left one). | + | The answer is 14. First, find the area of the semicircle by squaring the radius of the larger circle, multiplying it by pi, and dividing by 2. to find the grey parts in between the semi-circles, create a shape using two-quarter circles with radius's of 1 on the outside, and a rectangle with sides 2 and 1. Find the area, then subtract that area by two semicircles with a radius of 1. The difference would give you the grey area, then multiply the difference by two since there are two of them, the area is 4. Next, construct a 30, 60, 90 triangle using a line drawn from point F, intersecting the circle with a radius of 2 and a semicircle with radius 1 (it could be either the right or left one). |
| + | - I can't really word the rest without a picture, so if the rest of you editors can find a picture of the problem I would greatly appreciate it. -lialan2004 | ||
Revision as of 23:54, 13 February 2019
The answer is 14. First, find the area of the semicircle by squaring the radius of the larger circle, multiplying it by pi, and dividing by 2. to find the grey parts in between the semi-circles, create a shape using two-quarter circles with radius's of 1 on the outside, and a rectangle with sides 2 and 1. Find the area, then subtract that area by two semicircles with a radius of 1. The difference would give you the grey area, then multiply the difference by two since there are two of them, the area is 4. Next, construct a 30, 60, 90 triangle using a line drawn from point F, intersecting the circle with a radius of 2 and a semicircle with radius 1 (it could be either the right or left one). - I can't really word the rest without a picture, so if the rest of you editors can find a picture of the problem I would greatly appreciate it. -lialan2004
