Problem 52589. Circular Segment Area

Created by minnolina

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Let us consider a circle with radius </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r&gt;0</w:t></w:r></w:customXml><w:r><w:t>. If we draw an angle </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>t \\in [0,\\pi]</w:t></w:r></w:customXml><w:r><w:t> (in radians) from the center of the circle, the two radii forming that angle intersect the circle at </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>B</w:t></w:r></w:customXml><w:r><w:t>. We call </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a\\ge0</w:t></w:r></w:customXml><w:r><w:t> the area delimited by the chord and the arc </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>AB</w:t></w:r></w:customXml><w:r><w:t> (the so-called Circular Segment, blu in the figure). </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=\"175\"/><w:attr w:name=\"width\" w:val=\"161\"/><w:attr w:name=\"verticalAlign\" w:val=\"middle\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For a given radius </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r</w:t></w:r></w:customXml><w:r><w:t> and area </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t>, compute the angle </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>t</w:t></w:r></w:customXml><w:r><w:t> (rounded to 6 significant 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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<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: 276.619px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 138.31px; transform-origin: 406.996px 138.31px; vertical-align: baseline; "><div style="block-size: 62.7273px; 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: 383.991px 31.3636px; text-align: left; transform-origin: 383.999px 31.3636px; 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; ">Let us consider a circle with radius <img src="data:image/png;base64,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" width="35.5" height="17.5" style="width: 35.5px; height: 17.5px;"><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; ">. If we draw an angle <img src="data:image/png;base64,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" width="59.5" height="17.5" style="width: 59.5px; height: 17.5px;"><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; "> (in radians) from the center of the circle, the two radii forming that angle intersect the circle at A<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; "> and B<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; ">. We call <img src="data:image/png;base64,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" width="36.5" height="17.5" style="width: 36.5px; height: 17.5px;"><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; "> the area delimited by the chord and the arc <img src="data:image/png;base64,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" width="23" height="17.5" style="width: 23px; height: 17.5px;"><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; "> (the so-called Circular Segment, blu in the figure). </div><div style="block-size: 175px; 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: 383.991px 87.5px; text-align: left; transform-origin: 383.999px 87.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" width="161" height="175" style="vertical-align: middle;width: 161px;height: 175px" 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" data-image-state="image-loaded"></div><div style="block-size: 20.9091px; 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: 383.991px 10.4545px; text-align: left; transform-origin: 383.999px 10.4545px; 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; ">For a given radius r<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; "> and area a<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; ">, compute the angle t<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; "> (rounded to 6 significant digits).</div></div></div>

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Last Solution submitted on Apr 30, 2022

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1 Comment

Nikolaos Nikolaou on 16 Oct 2021

nice problem :)

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basic geometry

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Problem 52589. Circular Segment Area

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Problem 52589. Circular Segment Area

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