[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207774-en":3,"doc-seo-207774-105":30,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207774,2336475104042,"Tawan","https://ap-avatar.wpscdn.com/avatar/22000c4c32af1715be0?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786537525561427321",4,"Exam","AQA GCSE Maths - Circle Theorems Revision Notes","Revision notes for AQA GCSE Maths on circle theorems, focusing on angle facts involving centres, semicircles, chords, and tangents. Covers key definitions of circle parts such as radius, diameter, arc, sector, chord, segment, and tangent, and links theorem use to common exam-style reasoning. Includes essential formulae for circumference and area, an exam tip for annotating diagrams, and worked example guidance alongside step-by-step identification strategies.","Head to www.savemyexams. com for more awesome resources  \n AQA GCSE Maths  \nCircle Theorems  \nContents  \n Angles at Centre & Semicircles  Chords & Tangents  \n Cyclic Quadrilaterals  Segment Theorems  Circle Theorem Proofs  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nAngles at Centre & Semicircles  \nWhat are circle theorems?  \n You will have learned a lot of angle facts foryour GCSE, including angles in polygons and angles with parallel lines  \n Circle Theorems deal with angle facts that occur when lines are drawn within and connected to a circle What doI need to know?  \n You must be familiar with the names of parts of a circle including radius, diameter, arc, sector, chord, segment and tangent  \nTo solve some problems you may need to use the angle facts you are already familiar with from triangles, polygons, and parallel lines  \n You may also have to use the formulae for circumference and area, so ensure you’re familiar with them  \n Circumference = π × diameter (C = πd)  \n Area = πr2 (A = πr2)  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nAngles at Centre & Circumference  \nCircle Theorem: The angle subtended by an arc atthe centre is twice the angle atthe circumference  \n This is one of the most useful circle theorems and forms a basis for many other angle facts within circles  \n In this theorem, the chords (radii) to the centre and the chords to the circumference are both drawn from (subtended by) the ends of the same arc  \n It is an easy circle theorem to spot on a diagram  \nSTEP 1  \nFind any two radii in the circle and follow them to the circumference  \nSTEP 2  \nSee if there are lines from those points going to any other point on the circumference  \n If you are asked for a reason in an exam and you use this theorem, use the key phrase;  \n \" The angle atthe centre is twice the angle atthe circumference \"  \nThis theorem can also happen when the ‘triangle parts’ overlap:  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nCircle theorem: The angle ina semicircle is a right angle  \n This is a special case of the angle atthe centre theorem above  \n The angle on the diameter = 180°  \n The angle atthe circumference = 90°  \n It is easy to spot, look for a diameter in the circle and see if it makes the base of a triangle, with its top vertex atthe circumference  \n Make sure that you are looking at a diameter by checking it goes through the centre  \n These questions only need half of the circle so they could appear in whole circles or in semicircles only  \n Any angle atthe circumference that comes from each end of the diameter in this way will be 90°  \n This is most commonly known asthe angle in a semicircle theorem, however if you are asked fora reason in an exam and you use this theorem, use the key phrase;  \n \" The angle in a semicircle is 90° \"  \n Look out for triangles hidden among other lines/shapes within the circle  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nExam Tip  \n Add anything you can toa diagram you have been given  \n Mark any equal radii and write in any angles and lengths you can work out, even if they don’t seem relevant to the actual question  \n Questions often ask for “reasons” and the names/titles/phrases for each of these is exactly what they are after  \n When asked to “give reasons” aim to quote an angle fact or circle theorem for every angle you |nd, not just one for the |nal answer  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \n Worked example  \nFind the value of x in the d","cbCaikhKY3cl21wA","https://ap.wps.com/l/cbCaikhKY3cl21wA","pdf",3634521,1,37,"English","en",105,"# Circle Theorems\n## Angles at Centre & Semicircles\n## Angles at Centre & Circumference\n## Circle theorem: The angle in a semicircle is a right angle\n## Exam Tip\n## Worked example\n## Using the circle theorem to form an equation\n## Chords & Tangents\n## Circles & Chords\n## Circle Theorem: The perpendicular bisector of a chord is a radius","[{\"question\":\"What are circle theorems in GCSE Maths?\",\"answer\":\"Circle theorems are rules about angle facts that occur when lines are drawn within and connected to a circle. They help solve questions that ask for angles and reasons.\"},{\"question\":\"What is the key phrase for the centre and circumference angle theorem?\",\"answer\":\"Use: “The angle at the centre is twice the angle at the circumference”. This theorem relies on drawing the relevant chord lines from the ends of the same arc.\"},{\"question\":\"What is the circle theorem for a semicircle?\",\"answer\":\"The theorem states that the angle in a semicircle is a right angle. When asked for a reason, use the phrase “The angle in a semicircle is 90°”, and verify the base is a diameter through the centre.\"}]","AQA GCSE Maths - Circle Theorems Revision Notes | PDF",1788601102,93,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"aqa-gcse-maths-circle-theorems-revision-notes","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/aqa-gcse-maths-circle-theorems-revision-notes/207774/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What are circle theorems in GCSE Maths?","Question",{"text":74,"@type":75},"Circle theorems are rules about angle facts that occur when lines are drawn within and connected to a circle. They help solve questions that ask for angles and reasons.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What is the key phrase for the centre and circumference angle theorem?",{"text":79,"@type":75},"Use: “The angle at the centre is twice the angle at the circumference”. This theorem relies on drawing the relevant chord lines from the ends of the same arc.",{"name":81,"@type":72,"acceptedAnswer":82},"What is the circle theorem for a semicircle?",{"text":83,"@type":75},"The theorem states that the angle in a semicircle is a right angle. 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