Problem 49913. Splitting Square - 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 square, determine the radius of the circle defining the red 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 2 to 3, then these two numbers will be the first two numbers in the input. The last entry is the side of the square. Please keep in mind that if the radius of the circle is larger than the side of the square, then the red region is defined by the overlapping area between the circle and the square (as shown in the figure below).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"251\"/><w:attr w:name=\"width\" w:val=\"295\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" 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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: 696px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 348px; transform-origin: 407px 348px; 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: 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data-image-state="image-loaded"></div><div style="block-size: 126px; 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 63px; text-align: left; transform-origin: 384px 63px; 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 square is to be split into two regions (e.g., red and blue). Given the ratio between the two regions and the side of the square, determine the radius of the circle defining the red 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 2 to 3, then these two numbers will be the first two numbers in the input. The last entry is the side of the square. Please keep in mind that if the radius of the circle is larger than the side of the square, then the red region is defined by the overlapping area between the circle and the square (as shown in the figure below).</span></span></div><div style="block-size: 257px; 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 128.5px; text-align: left; transform-origin: 384px 128.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" width="295" height="251" style="vertical-align: baseline;width: 295px;height: 251px" 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data-image-state="image-loaded"></div></div></div>

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Last Solution submitted on Jan 20, 2023

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1 Comment

Rafael S.T. Vieira on 30 Oct 2022

This problem needs more tests. Many answers do not solve this problem at all. The ratio needs to be bigger than pi/4 to be difficult.

For instance, a circle obeying this vector s=[100 1 1] should have a radius of 1.3160, which is less than sqrt(2).

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Problem 49913. Splitting Square - Problem the third

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Problem 49913. Splitting Square - Problem the third

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