e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
110 lines
5.7 KiB
HTML
110 lines
5.7 KiB
HTML
<!doctype html>
|
|
<html lang="en"><!-- #BeginTemplate "/Templates/Advanced.dwt" --><!-- DW6 -->
|
|
|
|
<!-- Mirrored from www.mathsisfun.com/geometry/circle-intersect-secants-angle.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:07 GMT -->
|
|
<head>
|
|
<!-- #BeginEditable "doctitle" -->
|
|
<title>Angle of Intersecting Secants Theorem</title>
|
|
<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents." />
|
|
<!-- #EndEditable -->
|
|
<meta name="keywords" content="math, maths, mathematics, school, homework, education" />
|
|
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
|
|
<meta name="viewport" content="width=device-width; initial-scale=1.0; user-scalable=true;" />
|
|
<meta name="HandheldFriendly" content="true"/>
|
|
<meta http-equiv="pics-label" content='(PICS-1.1 "http://www.classify.org/safesurf/" L gen true for "http://www.mathsisfun.com" r (SS~~000 1))' />
|
|
<meta name="referrer" content="always">
|
|
<link rel="stylesheet" type="text/css" href="../style3.css" />
|
|
<script src="../main3.js" type="text/javascript"></script>
|
|
</head>
|
|
|
|
<body id="bodybg" class="adv">
|
|
<div class="bg">
|
|
<div id="stt"></div>
|
|
<div id="hdr"></div>
|
|
<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun" /></a></div>
|
|
<div id="advText">Advanced</div>
|
|
<div id="gtran"><script type="text/javascript">document.write(getTrans());</script></div>
|
|
<div id="gplus"><script type="text/javascript">document.write(getGPlus());</script></div>
|
|
<div id="adTopOuter" class="centerfull noprint">
|
|
<div id="adTop">
|
|
<script type="text/javascript">document.write(getAdTop());</script>
|
|
</div>
|
|
</div>
|
|
<div id="adHide">
|
|
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
|
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
|
<a href="../about-ads.html">About Ads</a></div>
|
|
</div>
|
|
<div id="menuWide" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(0));</script>
|
|
</div>
|
|
<div id="linkto">
|
|
<div id="linktort"><script type="text/javascript">document.write(getLinks());</script></div>
|
|
</div>
|
|
<div id="search" role="search"><script type="text/javascript">document.write(getSearch());</script></div>
|
|
<div id="menuSlim" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(1));</script>
|
|
</div>
|
|
<div id="menuTiny" class="menu">
|
|
<script type="text/javascript">document.write(getMenu(2));</script>
|
|
</div>
|
|
<div id="extra"></div>
|
|
</div>
|
|
<div id="content" role="main"><!-- #BeginEditable "Body" -->
|
|
|
|
<h1 class="center">Angle of Intersecting Secants</h1>
|
|
<p>This is the idea (a,b and c are angles):</p>
|
|
<p class="center"><img src="images/circle-intersect-angle.svg" alt="Angle of Intersecting Secants" ></p>
|
|
<p>And here it is with some actual values:</p>
|
|
<p class="center"><img src="images/circle-intersect-angle-ex.svg" alt="Angle of Intersecting Secants example" ></p>
|
|
<p>In words: <i>the angle made by two <a href="tangent-secant-lines.html">secants</a> (a line that cuts a circle at two points) that <b>intersect outside</b> the circle is half of the furthest arc minus the nearest arc.</i></p>
|
|
<p> </p>
|
|
<p class="center larger">Why not try drawing one yourself, measure it using a protractor, <br>
|
|
and see what you get?</p>
|
|
<p> </p>
|
|
<p>It also works when either line is a <a href="tangent-secant-lines.html">tangent</a> (a line that just touches a circle at one point). Here we see the "both are tangents" case:</p>
|
|
<p class="center"><img src="images/circle-intersect-angle-ex2.svg" alt="Angle of Intersecting Secants example" ></p>
|
|
<p>That's it! You know it now.</p>
|
|
<p> </p>
|
|
<div class="fun">
|
|
<h3>But How Come?</h3>
|
|
<p>Is this magic?</p>
|
|
<p>Well, we can prove it if you want:</p>
|
|
<p>AC and BD are two secants that intersect at the point P outside the circle. What is the relationship between the angle CPD and the arcs AB and CD?</p>
|
|
<p class="center"><img src="images/lines-circle-sec-sec-detail.svg" alt="Two lines intersecting a circle where vertex is inside the circle "></p>
|
|
<p>We start by saying that the angle subtended by arc CD at O is <b>2θ</b> and the arc subtended by arc AB at O is <b>2Φ </b></p>
|
|
<p>By the <a href="circle-theorems.html">Angle at the Center Theorem</a>: </p>
|
|
<p class="so">∠DAC = ∠DBC = θ and ∠ADB = ∠ACB = Φ </p>
|
|
<p>And PAC is 180°, so:</p>
|
|
<p class="so">∠DAP = 180° − θ </p>
|
|
<p>Now use <a href="../proof180deg.html">angles of a triangle add to 180°</a> in triangle APD: </p>
|
|
<p class="so">∠CPD = 180° − (∠DAP + ∠ADP) </p>
|
|
<p class="so">∠CPD = 180° − (180° − θ + Φ) = θ − Φ</p>
|
|
<p class="so">∠CPD = θ − Φ</p>
|
|
<p class="so">∠CPD = ½(2θ − 2Φ) </p>
|
|
<p>Done! </p>
|
|
</div>
|
|
<p> </p>
|
|
<div class="questions">
|
|
<script type="text/javascript">getQ(7385, 7386, 7387, 7388, 7389, 13611, 13612, 13613, 13614, 13615);</script>
|
|
</div>
|
|
<div class="related">
|
|
<a href="tangent-secant-lines.html">Tangent and Secant Lines</a> <a href="index.html">Geometry Index</a>
|
|
</div>
|
|
<!-- #EndEditable --></div>
|
|
<div id="adend" class="centerfull noprint">
|
|
<script type="text/javascript">document.write(getAdEnd());</script>
|
|
</div>
|
|
<div id="footer" class="centerfull noprint">
|
|
<script type="text/javascript">document.write(getFooter());</script>
|
|
</div>
|
|
<div id="copyrt">
|
|
Copyright © 2018 MathsIsFun.com
|
|
</div>
|
|
|
|
<script type="text/javascript">document.write(getBodyEnd());</script>
|
|
</body>
|
|
<!-- #EndTemplate -->
|
|
<!-- Mirrored from www.mathsisfun.com/geometry/circle-intersect-secants-angle.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:44:08 GMT -->
|
|
</html>
|