[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207775-en":3,"doc-seo-207775-105":30,"detail-sidebar-cat-0-en-105":91},{"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":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},207775,2336475104362,"Mali","https://ap-avatar.wpscdn.com/avatar/22000c4c46a41b752dd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786595829695023868",4,"Exam","Circle Theorems (H) - Maths GCSE Sample and Specimen Questions","A collection of 9 math GCSE sample and specimen questions focused on circle theorems, including calculations involving angles formed by tangents, radii/diameters, and reflex angles. Learners are asked to calculate unknown angles, prove angle relationships, and work with regular polygon geometry on circles. Several questions require clear step-by-step reasoning, checking true/false statements, and using established circle properties for justification across different awarding bodies.","Circle Theorems (H)  \nA collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas.  \n\n| Name: |  |\n| --- | --- |\n| Total Marks: |  |\n\n1. (a) Calculate the size of the angle marked x. You must give a reason for your answer.  \n[2]  \n(b) The diagram shows a circle with centre O.  \nThe tangent PT touches the circle at C.  \nThe reflex angle at the centre of the circle is 280° .  \nDiagram not drawn to scale  \nFind the size of 􀜤̂􀜣􀜥 .  \nYou must give a reason for your answer.  \n[2]  \n(c) The points A, B and C lie on the circumference of a circle.  \nThe straight line PBT is a tangent to the circle.  \nCBP = 􀝔 , where 􀝔 is measured in degrees.  \nShow that the size of ABC in degrees is 90 − 12 􀝔 You must give reasons for each step of your answer.  \n[2]  \n2. 􀜣 , 􀜤 and 􀜥 are points on a circle.  \n􀁸 􀜤􀜥 bisects angle 􀜣􀜤􀜳 .  \n􀁸 􀜲􀜤􀜳 is a tangent to the circle.  \nAngle 􀜥􀜤􀜳 = 􀝔  \nProve that 􀜣􀜥 = 􀜤􀜥  \n[3]  \n3. A, B, C and D are points on the circumference of a circle, centre O.  \nAC is a diameter of the circle.  \nAngle ABD = 58° .  \nAngle CDB = 22° .  \nWork out the sizes of angle ACD and ACB, giving reasons for your answers.  \n(a) Angle ACD = . . . . . . . . . . . . . . . . . . . . . . . . . . .° [2]  \n(b) Angle ACB = . . . . . . . . . . . . . . . . . . . . . . . . . . .° [3]  \n4.  \nS and T are points on the circumference of a circle, centre O.  \nPT is a tangent to the circle.  \nSOP is a straight line.  \nAngle OPT = 32°  \nWork out the size of the angle marked x.  \nYou must give a reason for each stage of your working.  \n[4]  \n5. The diagram shows a circle, centre O.  \nPoints P, Q, R and S lie on the circumference of the circle.  \nUST is a tangent to the circle.  \nAngle RPS = 44o and angle PSO = 32o.  \na) Work out the value of x .  \na) x = ...................................... [4]  \nb) Work out the value of y .  \nb) y = ...................................... [3]  \n6.  \n􀜲􀜳􀜴􀜵􀜶 is a regular pentagon.  \n􀜴 , 􀜷 and 􀜶 are points on a circle, centre 􀜱 .  \n􀜳􀜴 and 􀜲􀜶 are tangents to the circle.  \n􀜴􀜵􀜷 is a straight line.  \nProve that 􀜵􀜶 = 􀜷􀜶 .  \n[5]  \n7. A, B and C are points on the circumference of a circle centre O.  \nProve that angle BOC is twice the size of angle BAC.  \n[4]  \n8. B, C and D are points on a circle.  \nAngle ABC = 92°  \nAngle ACB = 38°  \nAngle ACD = 50°  \nAngle CDE = 32°  \nTick whether each statement is true or false. Give a reason for each answer.  \nReason  \nReason  \nReason  \nReason  \n[4]  \nCREDITS AND NOTES  \n\n| Question | Awarding Body |\n| --- | --- |\n| 1 | WJEC Eduqas |\n| 2 | AQA |\n| 3 | OCR |\n| 4 | Pearson Edexcel |\n| 5 | OCR |\n| 6 | Pearson Edexcel |\n| 7 | Pearson Edexcel |\n| 8 | AQA |\n\nNotes:  \nThese questions have been retyped from the original sample/specimen assessment materials and whilst every effort has been made to ensure there are no errors, any that do appear are mine and not the exam board s (similarly any errors I have corrected from the originals are also my corrections and not theirs!) .  \nPlease also note that the layout in terms of fonts, answer lines and space given to each question does not reflect the actual papers to save space.  \nThese questions have been collated by me as the basis for a GCSE working party set up by the GLOW maths hub - if you want to get involved please get in touch. The objective is to provide support to fellow teachers and to give you a flavour of how different topics “could” be examined. They should not be used to form a decision as to which board to use. There is no guarantee that a topic will or won’t appear in the “live” papers from a specific exam board or that examination of a topic will be as shown in these questions.  \nLinks:  \nAQA [http://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300](http://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300)  \nOCR [http://ocr.org.uk/gcsemaths](http://ocr.org.uk/gcsemaths)  \nPearson Edexcel [http://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html](http://","cbCailGLOlQ90wpT","https://ap.wps.com/l/cbCailGLOlQ90wpT","pdf",527609,1,8,"English","en",105,"# Circle Theorems (H)\n## Questions 1-8\n## Credits and Notes","[{\"question\":\"What types of tasks are included in Circle Theorems (H)?\",\"answer\":\"The document includes angle calculations, proof of angle relationships, and a true/false question set where reasons must be given for each answer.\"},{\"question\":\"How are tangents used in these circle theorem questions?\",\"answer\":\"Tangent lines are used to form angle relationships with the circle, such as angles between tangents and chords or with lines from the centre, requiring reasoning for each step.\"},{\"question\":\"Which awarding bodies provide the sample and specimen questions?\",\"answer\":\"The questions are credited to WJEC Eduqas, AQA, OCR, and Pearson Edexcel, with the credits section listing which board corresponds to each question number.\"}]","Circle Theorems (H) - Maths GCSE Sample and Specimen Questions | PDF",1788601104,20,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"circle-theorems-h-maths-gcse-sample-and-specimen-questions","",{"@graph":36,"@context":85},[37,53,68],{"@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/circle-theorems-h-maths-gcse-sample-and-specimen-questions/207775/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-07","2026-09-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What types of tasks are included in Circle Theorems (H)?","Question",{"text":75,"@type":76},"The document includes angle calculations, proof of angle relationships, and a true/false question set where reasons must be given for each answer.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are tangents used in these circle theorem questions?",{"text":80,"@type":76},"Tangent lines are used to form angle relationships with the circle, such as angles between tangents and chords or with lines from the centre, requiring reasoning for each step.",{"name":82,"@type":73,"acceptedAnswer":83},"Which awarding bodies provide the sample and specimen questions?",{"text":84,"@type":76},"The questions are credited to WJEC Eduqas, AQA, OCR, and Pearson Edexcel, with the credits section listing which board corresponds to each question number.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,104,109,114,119,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":102,"slug":103},70,"exam",{"id":105,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":29,"slug":126},9,"Religion & Spirituality","religion-spirituality",{"id":29,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":29,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]