[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207772-en":3,"doc-seo-207772-105":31,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},207772,962085320529,"Sarah ","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",4,"Exam","CIRCLE THEOREMS - Edexcel GCSE Mathematics (Linear) - 1MA0","Exam practice material for Edexcel GCSE Mathematics (Linear) 1MA0 focused on circle theorems and related angle problems. The questions cover angles formed by chords, radii, tangents, and diameters, including requirements to find specific angles and provide reasons for each working step. Some tasks reference diagrams that are not accurately drawn, emphasizing geometric reasoning and correct application of tangent-radius and angle-chord relationships.","Edexcel GCSE  \nMathematics (Linear)– 1MA0  \nCIRCLE THEOREMS  \nMaterials required for examination Items included with question papers  \nRuler graduated in centimetres and Nil  \nmillimetres, protractor, compasses, pen, HB pencil, eraser.  \nTracing paper may be used.  \nInstructions  \nUse black ink or ball-point pen.  \nFill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions.  \nAnswer the questions in the spaces provided – there may be more space than you need. Calculators may be used.  \nInformation  \nThe marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.  \nQuestions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed – you should take particular care on these questions with your spelling, punctuation and grammar, as well as the clarity of expression.  \nAdvice  \nRead each question carefully before you start to answer it. Keep an eye on the time.  \nTry to answer every question.  \nCheck your answers if you have time at the end.  \n1.  \nA, B, C and D are points on the circumference of a circle.  \nAngle ABD = 54􀁱 .  \nAngle BAC = 28􀁱 .  \n(i) Find the size of angle ACD.  \n°  \n........................  \n(ii) Give a reason for your answer.  \n(3 marks)  \n2.  \nDiagram NOT accurately drawn  \nA, B, C and D are points on the circumference of a circle, centre O.  \nAngle AOC = 168􀁱  \nWork out the size of angle ADC.  \nYou must give reasons for your working.  \n􀁱  \n(4 marks)  \n3.  \nA, B and D are points on the circumference of a circle, centre O.  \nBOD is a diameter of the circle.  \nBC and AC are tangents to the circle.  \nAngle OCB = 34° .  \nWork out the size of angle DOA.  \n°  \n..........................................  \n(4 marks)  \n4.  \nDiagram NOT accurately drawn  \nB and C are points on a circle, centre O.  \nAB and AC are tangents to the circle.  \nAngle BOC = 130° .  \nWork out the size of angle BAO.  \n°  \n..............................  \n(4 marks)  \n5.  \nDiagram NOT accurately drawn  \nA and B are points on the circumference of a circle, centre O.  \nPA and PB are tangents to the circle.  \nAngle APB is 86° .  \nWork out the size of the angle marked x.  \n°  \n.........................  \n(3 marks)  \n6.  \nS T  \nDiagram NOT accurately drawn  \nR and S are two points on a circle, centre O.  \nTS is a tangent to the circle.  \nAngle RST= x.  \nProve that angle ROS = 2x.  \nYou must give reasons for each stage of your working.  \n(4 marks)  \n7.  \nIn the diagram, O is the centre of the circle.  \nA and C are points on the circumference of the circle.  \nBCO is a straight line.  \nBA is a tangent to the circle.  \nAB = 8 cm.  \nOA = 6 cm.  \n(a) Explain why angle OAB is a right angle.  \n........................................................................................................................... ..........................  \n............................................................................................................................. ........................  \n(1)  \n(b) Work out the length of BC.  \n................................cm  \n(3)  \n (4 marks)  \n8.  \nA, B, C and D are points on a circle, centre O.  \nBC = CD.  \nAngle BCD = 130° .  \n(a) Write down the size of angle BAD.  \nGive a reason for your answer.  \n°  \n...................................  \n(2)  \n(b) Work out the size of angle ODC.  \nGive reasons for your answer.  \n°  \n...................................  \n(4)  \n (6 marks)  \n9.  \nDiagram NOT accurately drawn  \nIn the diagram, A, B, C and D are points on the circumference of a circle, centre O.  \nAngle BAD = 70° .  \nAngle BOD = x° .  \nAngle BCD = y° .  \n(a) (i) Work out the value of x.  \nx =    \n(ii) Give a reason for your answer.  \n............................................................................................................................. ..  \n......................................................................................................","cbCaigyrrOyF8PSw","https://ap.wps.com/l/cbCaigyrrOyF8PSw","pdf",252417,2,1,12,"English","en",105,"# Circle angle questions\n## Tangents and angles\n## Chords, radii and diameters\n## Proof using circle theorems","[{\"question\":\"What is the main topic of these questions?\",\"answer\":\"The questions focus on circle theorems, especially finding angles in configurations involving points on a circle, chords, tangents, radii, and diameters.\"},{\"question\":\"Why are some diagrams labelled as “NOT accurately drawn”?\",\"answer\":\"The exact measurements in the diagram are not reliable, so answers must be obtained using circle theorem relationships and correct reasoning rather than reading angles from the drawing.\"},{\"question\":\"How should answers be presented in these questions?\",\"answer\":\"Many questions require reasons for each stage of working, so students should state the relevant circle theorem or angle fact used to reach the result.\"}]","CIRCLE THEOREMS - 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