{"id":227527,"date":"2025-06-06T07:40:39","date_gmt":"2025-06-06T07:40:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227527"},"modified":"2025-06-06T07:40:41","modified_gmt":"2025-06-06T07:40:41","slug":"two-circles-two-circles-on-a-cartesian-plane-a-and-b-are-each-defined-by-three-descriptors-x-the-x-coordinate-of-the-circles-center","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/two-circles-two-circles-on-a-cartesian-plane-a-and-b-are-each-defined-by-three-descriptors-x-the-x-coordinate-of-the-circles-center\/","title":{"rendered":"Two Circles Two circles on a Cartesian plane, A and B, are each defined by three descriptors: \u2022 X: the x-coordinate of the circle’s center"},"content":{"rendered":"\n
Two Circles Two circles on a Cartesian plane, A and B, are each defined by three descriptors: \u2022 X: the x-coordinate of the circle’s center \u2022 Y: the y-coordinate of the circle’s center \u2022 R: the radius of the circle Circles A and B will both be centered either on the X-axis (i.e. YA = 0 and YB = 0), or on the Y-axis (i.e. XA = 0 and XB = 0), but not both. A pair of circles (A and B) will have one of the following relationship types: \u2022 Touching: they touch each other at a single point \u2022 Concentric: they have the same center point \u2022 Intersecting: they intersect each other (touching at two points) \u2022 Disjoint-Outside: disjoint with one existing outside of the other \u2022 Disjoint-Inside: disjoint with one contained inside the other (but not concentric) Example: circlePairs = [’30 105 03′, ’01 40 15′] Each string has 6 integers that represent X, Y, and R for circle.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
We are given two circles defined as strings in the form 'X Y R'<\/code>, where:<\/p>\n\n\n\n
\n
X<\/code> is the x-coordinate of the center<\/li>\n\n\n\n
Y<\/code> is the y-coordinate of the center<\/li>\n\n\n\n
R<\/code> is the radius<\/li>\n<\/ul>\n\n\n\n
The two circles given are:<\/p>\n\n\n\n
\n
'30 105 03'<\/code> \u2192 Circle A: X=30, Y=105, R=3<\/li>\n\n\n\n
'01 40 15'<\/code> \u2192 Circle B: X=1, Y=40, R=15<\/li>\n<\/ol>\n\n\n\n
Let\u2019s extract the values:<\/p>\n\n\n\n
\n
Circle A: center at (30, 105), radius = 3<\/li>\n\n\n\n
Circle B: center at (1, 40), radius = 15<\/li>\n<\/ul>\n\n\n\n
First, verify axis alignment:<\/p>\n\n\n\n
\n
Both circles have non-zero x and y<\/strong>, but to follow the problem constraints (centers lie either<\/em> on the X-axis or Y-axis), we must assume<\/strong> either:\n
\n
X-axis case: YA = 0 and YB = 0 \u2192 Not true (since YA = 105, YB = 40)<\/li>\n\n\n\n
Y-axis case: XA = 0 and XB = 0 \u2192 Not true (since XA = 30, XB = 1)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
However, the question may have a typo, or we assume the values were read with missing zeros. Possibly:<\/p>\n\n\n\n
Circle B is entirely inside Circle A, but their edges do not touch. Thus, they are disjoint inside<\/strong>.<\/p>\n\n\n\n\n\n\n\n
Final Answer: Disjoint-Inside<\/strong> \u2705<\/h3>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Two Circles Two circles on a Cartesian plane, A and B, are each defined by three descriptors: \u2022 X: the x-coordinate of the circle’s center \u2022 Y: the y-coordinate of the circle’s center \u2022 R: the radius of the circle Circles A and B will both be centered either on the X-axis (i.e. YA = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-227527","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227527","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=227527"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227527\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227527"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227527"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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<\/figure>\n","protected":false},"excerpt":{"rendered":"