[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207770-en":3,"doc-seo-207770-105":29,"detail-sidebar-cat-0-en-105":89},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":20,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},207770,687207022233,"Connor ","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",4,"Exam","GCSE Circle Theorems","This document serves as a comprehensive revision poster for GCSE Circle Theorems, designed to aid students in their exam preparation. It systematically outlines and explains seven key theorems with accompanying diagrams for visual clarity. Each theorem is presented with its core statement and illustrative figures, covering concepts such as the angle between a tangent and radius, angles in a semicircle, diameter bisecting chords, the relationship between central and circumference angles, equal tangents from a point, intersecting chords, and the alternate segment theorem. The poster also includes visual representations for exterior intersecting chords and a formulaic representation for their lengths. A dedicated section for IGCSE students highlights specific content relevant to their curriculum. Additional resources for further learning are provided through website links to Addvance Maths for online tutorials and revision materials, reinforcing the learning of these fundamental geometrical principles relevant to intermediate-level mathematics.","\\\\  \nGCSE Circle Theorems  \nLabelling the  \nParts of a Circle  \nA  \nwith  \nx  \nTheorem 1:  \ntangent to a circle makes a right-angle  \nthe radius.  \nTheorem 2:  \nThe Angle in a Semicircle is a Right-Angle.  \nx  \nx  \n􀜽  \nx  \n􀝊  \nTheorem 5:  \nTangents from the same point are equal length.  \nx  \nIntersecting Chords  \nFor IGCSE Only  \n􀜾  \nTheorem 3:  \nA diameter bisects a chord at right  \n2  \n2  \nangles.  \n􀜽  \nTheorem 4: The Arrow Head Theorem  \nThe angle at the subtended at the centre of a circle is double the angle subtended at the circumference.  \n􀜾  \n􀝉  \nTheorem 7: The Alternate Segment Theorem  \nThe angle between a tangent and a chord is equal to the angle subtended by the ends of the chord in the alternate segment.  \n􀜾  \n􀜿  \n􀝀  \n􀜽  \n􀜾  \n􀜿  \n􀝀  \nExterior Intersecting Chords  \n􀜽􀜾 = 􀜿􀝀  \nLearn more at  \n[www.youtube.com/c/AddvanceMaths](www.youtube.com/c/AddvanceMaths)  \n[www.addvancemaths.com/revision/circletheorems](www.addvancemaths.com/revision/circletheorems)","cbCaimTY1mAmOxzr","https://ap.wps.com/l/cbCaimTY1mAmOxzr","pdf",2205822,1,"English","en",105,"# GCSE Circle Theorems\n## Labelling the Parts of a Circle\n## Theorem 1\n## Theorem 2\n## Theorem 3\n## Theorem 4\n## Theorem 5\n## Theorem 7\n## Intersecting Chords\n## Exterior Intersecting Chords","[{\"question\":\"What is Theorem 1 about?\",\"answer\":\"Theorem 1 states that a tangent to a circle makes a right-angle with the radius.\"},{\"question\":\"What is the relationship between the angle at the center and the angle at the circumference according to Theorem 4?\",\"answer\":\"Theorem 4, also known as the Arrowhead Theorem, states that the angle subtended at the center of a circle is double the angle subtended at the circumference.\"},{\"question\":\"How are tangents from the same point related, according to Theorem 5?\",\"answer\":\"Theorem 5 explains that tangents drawn from the same external point to a circle are of equal length.\"}]","GCSE Circle Theorems | 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is Theorem 1 about?","Question",{"text":73,"@type":74},"Theorem 1 states that a tangent to a circle makes a right-angle with the radius.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"What is the relationship between the angle at the center and the angle at the circumference according to Theorem 4?",{"text":78,"@type":74},"Theorem 4, also known as the Arrowhead Theorem, states that the angle subtended at the center of a circle is double the angle subtended at the circumference.",{"name":80,"@type":71,"acceptedAnswer":81},"How are tangents from the same point related, according to Theorem 5?",{"text":82,"@type":74},"Theorem 5 explains that tangents drawn from the same external point to a circle are of equal 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