[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207768-en":3,"doc-seo-207768-105":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},207768,549768072016,"WPS_1786070896","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",4,"Exam","Circle Theorems - IGCSE Cambridge (CIE) Maths Questions","A focused set of IGCSE Cambridge (CIE) Maths circle-theorem questions covering angles formed at the centre and circumference, angle relationships in a semicircle, and results involving chords and tangents. The questions require finding specific angles using tangent and chord properties, cyclic quadrilateral angle facts, and angle calculations with given degree measures. Both Medium and Hard sections include diagrams described by points on a circle, tangency conditions, parallel lines, and parallel chords, with total marks and part-wise marking guidance.","IGCSE  Cambridge (CIE)  Maths  1 hour  18 questions  \nCalculator Questions  \nCircle Theorems  \nAngles at Centre & Circumference / Angle in a Semicircle / Theorems with Chords & Tangents / Angles in Cyclic Quadrilaterals / Angles in the Same Segment / The Alternate Segment Theorem  \nMedium (6 questions) /26 Hard (7 questions) /37 Very Hard (5 questions) /21  \nTotal Marks /84  \nScan here to return to the course  \nor visit [savemyexams.com](savemyexams.com)  \nMedium Questions  \n1 (a)  \nIn the diagram, A, B, C and D lie on the circle, centre O.  \nEA is a tangent to the circle at A.  \nAngle EAB = 61° and angle BAC = 55° .  \nFind angle BAO.  \nAngle BAO = ................................................  \n(1 mark)  \n(b) Find angle AOC.  \nAngle AOC = ................................................  \n(2 marks)  \n(c) Find angle ABC.  \nAngle ABC = ................................................  \n(1 mark)  \n(d) Find angle CDA.  \nAngle CDA = ................................................  \n(1 mark)  \n2  \nA, B, C and D are points on the circumference of the circle, centre O. DOB is a straight line and angle DAC = 58° .  \nFind angle CDB.  \nAngle CDB = ...............................................  \n(3 marks)  \n3  \nP, Q and R are points on the circumference of the circle, centre O.  \nPO is parallel to QR and angle POQ = 48° .  \nFind angle OPR.  \nAngle OPR = ..............................................  \n(2 marks)  \n4 (a)  \nA, B, C, D and E lie on the circle, centre O.  \nAngle AEB = 35°, angle ODE = 28° and angle ACD = 109° .  \nWork out the following angles, giving reasons for your answers. i) Angle EBD = ............................. because .............................  \n[3]  \nii) Angle EAD = ............................. because .............................  \n[2]  \n(5 marks)  \n(b) Work out angle BEO.  \nAngle BEO = ................................................  \n(3 marks)  \n5  \nK, L and M are points on the circle.  \nKS is a tangent to the circle at K.  \nKM is a diameter and triangle KLM is isosceles.  \nFind the value of z .  \nz =    \n(2 marks)  \n6  \nF, G, H and J are points on the circle.  \nEFG is a straight line parallel to JH.  \nFind the value of y .  \ny = ................................................  \n(6 marks)  \nHard Questions  \n1  \nThe points A, B, C, D and E lie on the circle.  \nPAQ is a tangent to the circle at A and EC = EB.  \nAngle ECB = 80° and angle ABE = 40° .  \nFind the values of v, w , x, y and z .  \nv = ................... w = ................... x = ................... y = ................... z = ..................  \n(5 marks)  \n2  \nA, B, C and D are points on the circle, centre O.  \nEF is a tangent to the circle at D.  \nAngle ADE = 42° and angle COD = 162° .  \nFind the following angles, giving reasons for each of your answers.  \ni) Angle x  \nx =   because   [2]  \nii) Angle y  \ny = ............................ because ........................... [2]  \niii) Angle z  \nz =   because   [3]  \n(7 marks)  \n3  \nAT is a tangent to the circle at A.  \nFind the value of x .  \nx =    \n(2 marks)","cbCaioG5orb0mIYo","https://ap.wps.com/l/cbCaioG5orb0mIYo","pdf",2544439,1,19,"English","en",105,"# Circle Theorems\n## Medium Questions\n## Hard Questions","[{\"question\":\"What types of angle problems are included in these Circle Theorems questions?\",\"answer\":\"They include angles at the centre and circumference, angles in a semicircle, and angle relationships involving chords and tangents. Some questions also use properties of cyclic quadrilaterals and angles in the same segment.\"},{\"question\":\"How are tangents used in the questions?\",\"answer\":\"A tangent is given at specific points on the circle, and angle values are derived using tangent-angle relationships. For example, angles between a tangent and a chord are targeted to find unknown angles.\"},{\"question\":\"What distinguishes the Medium and Hard question sections?\",\"answer\":\"The document separates questions into a Medium section and a Hard section with higher complexity. Hard questions typically require finding multiple unknown angles and giving reasons based on several circle-theorem steps.\"}]","Circle Theorems - IGCSE Cambridge (CIE) Maths Questions | PDF",1788601089,48,{"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},"circle-theorems-igcse-cambridge-cie-maths-questions","",{"@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/circle-theorems-igcse-cambridge-cie-maths-questions/207768/",{"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 types of angle problems are included in these Circle Theorems questions?","Question",{"text":74,"@type":75},"They include angles at the centre and circumference, angles in a semicircle, and angle relationships involving chords and tangents. Some questions also use properties of cyclic quadrilaterals and angles in the same segment.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How are tangents used in the questions?",{"text":79,"@type":75},"A tangent is given at specific points on the circle, and angle values are derived using tangent-angle relationships. For example, angles between a tangent and a chord are targeted to find unknown angles.",{"name":81,"@type":72,"acceptedAnswer":82},"What distinguishes the Medium and Hard question sections?",{"text":83,"@type":75},"The document separates questions into a Medium section and a Hard section with higher complexity. 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