Problem 49943. Splitting Hexagon - Problem the third

Created by Doddy Kastanya

Solve Later

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Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the hexagon.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.jpeg","relationshipId":"rId1"}]},{"partUri":"/media/image1.jpeg","contentType":"image/jpeg","content":"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4RE6RXhpZgAATU0AKgAAAAgABAE7AAIAAAAlAAAISodpAAQAAAABAAAIcJydAAEAAABKAAAQ6OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEtBU1RBTllBIERvZGR5IC0gKE5TJkwpIC0gS0lORUNUUklDUwAAAAWQAwACAAAAFAAAEL6QBAACAAAAFAAAENKSkQACAAAAAzY3AACSkgACAAAAAzY3AADqHAAHAAAIDAAACLIAAAAAHOoAAAAIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 402px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 201px; transform-origin: 407px 201px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Consider a hexagon sitting in Quadrant I as depicted in an example below:</span></span></div><div style="block-size: 279px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 139.5px; text-align: left; transform-origin: 384px 139.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" data-image-state="image-loaded"></div><div style="block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">This hexagon is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the hexagon, determine the radius of the circle that splits the region. The ratio between the regions (red to blue) is presented through the first two entries in the input. For example, if the ratio is 1 to 2, then these two numbers will be the first two entries in the input. The last entry is the side of the hexagon.</span></span></div></div></div>

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Last Solution submitted on May 16, 2022

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easy geometry hexagon

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Problem 49943. Splitting Hexagon - Problem the third

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Problem 49943. Splitting Hexagon - Problem the third

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