{"id":61925,"date":"2021-05-28T12:33:16","date_gmt":"2021-05-28T10:33:16","guid":{"rendered":"https:\/\/wpcalc.com\/?p=61925"},"modified":"2025-05-09T08:10:20","modified_gmt":"2025-05-09T05:10:20","slug":"angle-bisector","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/angle-bisector\/","title":{"rendered":"Angle Bisector Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 class=\"text-lg font-display font-bold\">Bisector Between Two Lines Calculator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"61925\" data-favorite-title=\"Angle Bisector\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/angle-bisector\/\" data-favorite-excerpt=\"The Angle Bisector of Two Lines calculator determines the equations of the angle bisectors formed at the intersection of two lines. It\u2019s useful for solving problems in analytical geometry, design, and computer graphics. Simply enter the coefficients of the two lines, and the calculator will compute both angle bisectors: the one that divides the acute angle and the one for the obtuse angle.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/angle-bisector\/\" method=\"POST\" class=\"calculator\" id=\"calculator-61925\" data-post=\"61925\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Line r: a\u2081<\/label><input type=\"number\" name=\"line_r_a\" id=\"field-1\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Line r: b\u2081<\/label><input type=\"number\" name=\"line_r_b\" id=\"field-2\" placeholder=\"-1\" step=\"1\" value=\"-1\"\/><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Line r: c\u2081<\/label><input type=\"number\" name=\"line_r_c\" id=\"field-3\" placeholder=\"3\" step=\"1\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">Line s: a\u2082<\/label><input type=\"number\" name=\"line_s_a\" id=\"field-4\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">Line s: b\u2082<\/label><input type=\"number\" name=\"line_s_b\" id=\"field-5\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">Line s: c\u2082<\/label><input type=\"number\" name=\"line_s_c\" id=\"field-6\" placeholder=\"2\" step=\"1\" value=\"2\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"61925\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>First bisector<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Second bisector<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"61925\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">1<\/span><span class=\"reaction text-3xl\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">2<\/span><span class=\"reaction text-3xl\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">1<\/span><span class=\"reaction text-3xl\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Angle Bisector Equations Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">$$\\frac{|A_1x + B_1y + C_1|}{\\sqrt{A_1^2 + B_1^2}} = \\frac{|A_2x + B_2y + C_2|}{\\sqrt{A_2^2 + B_2^2}}$$<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where<\/strong>:<\/p>\n<ul>\n<li>$$A_1x + B_1y + C_1 = 0$$ and $$A_2x + B_2y + C_2 = 0$$ are the equations of the two lines.<\/li>\n<li>This equation yields two bisectors (one for each angle formed between the lines).<\/li>\n<li>The <strong>\u00b1<\/strong> versions of the equation represent the <strong>acute<\/strong> and <strong>obtuse<\/strong> angle bisectors.<\/li>\n<\/ul>\n<p>The result is one or two linear equations describing the bisecting lines.<br \/>\r\n<\/section>\n<p>In coordinate geometry, the bisector of the angle between two lines is the locus of points equidistant from the lines. This calculator automates the process of finding the bisectors using a formula derived from the distance of a point to a line. Applications include geometric design, optics, architectural layout, and CAD. You provide the general form equations of the two lines (Ax + By + C = 0), and the tool computes the equations for both angle bisectors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Angle Bisector of Two Lines calculator determines the equations of the angle bisectors formed at the intersection of two lines. It\u2019s useful for solving problems in analytical geometry, design, and computer graphics. Simply enter the coefficients of the two lines, and the calculator will compute both angle bisectors: the one that divides the acute angle and the one for the obtuse angle.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[23],"class_list":["post-61925","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61925","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=61925"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61925\/revisions"}],"predecessor-version":[{"id":63829,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61925\/revisions\/63829"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=61925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=61925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=61925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}