[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207781-en":3,"doc-seo-207781-105":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},207781,962085662650,"Dozel","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",4,"Exam","Circle Theorems Practice Questions - Angle Problems","Circle theorems practice questions focused on angle calculations involving points on a circle, a circle’s centre, tangents, and diameters. The tasks require finding specific angles such as ACD, ADC, DOA, BAO, and ODC, along with proving relationships like angle ROS equals 2x. Each question includes guidance to justify results using geometric facts (e.g., angles in triangles, properties of tangents, and supplementary angles).","DiagramNOT  \naccurately drawn  \nA,B,C and D are points on the circumference of a circle.Angle ABD=54.Angle BAC=28°.  \n(i)Find the size of angle ACD.  \n(ii)Give a reason for your answer.…   e…egneA……2Df….   ………………………………………………les…fro……neSa……int……ne  \n(3 marks)  \n   \n2.  \nDiagram NOT  \naccurately 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.  \ns oe     \n=8gle acentre;  \ncyolic quodri1a4a/  \n:18-8=9 o99.anle  in  \n\n| ………………  \u003Cbr>9   | ………………·  \u003Cbr>6   |\n| --- | --- |\n| (4 marks)   |  |\n\nDiagram NOT  \naccurately drayn  \nA,B and Dare points on the circumference of a circle,centre O.BOD is a diameter of the circle.  \nBC and AC are tangents to the circle.  \n90(tongenl weeł radiu)oBC0ACAngle OCB=34.  \nWork out the size of angle DOA.  \n=56  (Aryles iA triangle add h 180°)  \n(congruest friang(e⁴)AOC =Bo C180-56-56      68    (Anged on a shraigu4 kne =1f0°J  \n68  \n(4 marks)  \n   \n4.  \nA  \nDiagram NOT accurately drawn  \nB and C are points on a circle,centre O.AB and AC are tangents to the circle.Angle BOC=130°.  \nWork out the size of angle BAO.  \n…25  \n………  \n(4 marks)  \n   \nA and B are points on the circumference of a circle,centre O.PA and PB are tangents to the circle.Angle APB is 86°.  \nWork out the size of the angle marked x.  \n360-90-90-86 =94  \n6.  \nT  \nRand S are two points on a circle,centre O.TS is a tangent to the circle.Angle RST=x.  \nProve that angle ROS=2x.You must give reasons for each stage of your w  \n   \nP  \nDiagram NOT accurately drawn  \n…43…  \n(3marks)  \nDiagram NOT  \naccurately drawn  \n057二910°(+aungen woeh raoliu)90-xO5R90一x(;sosceles Axiangl-e)oks=Ros=180-90一j)-90～ng.  \n180-9o+x-90+x=2α  \n(4 marks)  \nDiagram NOT  \naccurately drawn  \nIn the diagram,O is the centre of the circle.A and C are points on the circumference of the circle.BCO is a straight line.BA is a tangent to the circle.AB=8cm.OA=6 cm.  \n(a)Explain why angle OAB is a right angle.  \n(1)  \n(b)Work out the length of BC.  \n(3)  \n(4 marks)  \n   \nA,B,C and Dare points on a circle,centre O.BC=CD.Angle BCD=130°.  \n(a)Write down the size of angle BAD.Give a reason for your answer.  \nadd to180°oppsite angleacyli qulate  \n5…  \n……..°  \n(2)  \n(b)Work out the size of angle ODC.Give reasons for your answer.  \n+Ciccu^revence  00=10°angle aer  sdocsle gl   \nadd uv 九 180So一 /O·anyles M quadilc)e。  \nCBo二  CD0  \n65  \n…….  \n(4)  \n(6marks)  \n   \nA  \nC  \nDiagram NOT accurately drawn  \nIn the diagram,A,B,C and D are points on the circumference of a circle,centre O.Angle BAD=70°.Angle BOD=x°.Angle BCD=y°.  \n(a)(i)  Work out the value of x.  \nx=………14  …………  \n(ii)Give a reason for your answer.  \n……an  ……cenr  …doub……         …………the…ciLcufere     ……………………    ………………………  \n(2)  \n(b)(i)  Work out the value ofy.  \ny=…………  ……………  \n)  \n(ii)Give a reason for your answer.  \n……2paa.sit……×Le.…      ……-gelac……………………9adcilt   …x    p……………80  \n(2)(4 marks)  \n   \nDiagram NOT  \naccurately drawn  \nThe diagram shows a circle centre O.  \nA,B and C are points on the circumference.  \nDCO is a straight line.DA is a tangent to the circle.  \nAngle ADO=36°  \n(a)Work out the size of angle AOD.  \n…54……。  \n(2)  \n(b)(i)Work out the size of angle ABC.  \n27  \n(ii)Give a reason for your answer  \nderen ce    …o…....           ..  .  \n(3)                                 (4 marks)  \nDiagram NOT  \naccurately drawn  \nB,D and E are points on a circle centre O.ABC is a tangent to the circle.BE is a diameter of the circle.Angle DBE=35°.  \n(a)Find the size of angle ABD.  \nGive a reason for your answer.adius it )a90°angewhere wherees  \n55  \n(2)  \n(b)Find the size of angle DEB.  \nGive a reason for your answer.nare segmen eoe  \n5。  \n(2)  \n(4 marks)  \n   \nB  \nP,Qand T are points on the circumference of a circle,centre O.The line ATB is the tangent at Tto the circle.  \nPQ=TQ.  \nAngle ATP=58°.  \nCalculate the size of angle OTQ.Give a reason for each stage in your working.  \nT= (Altecnote segnenh)  \nOTP:32tangelk  meetsradiusat9°age  \n90-58=32  \n180,ny","cbCaiqRNJVPEHrnv","https://ap.wps.com/l/cbCaiqRNJVPEHrnv","pdf",735573,1,11,"English","en",105,"# Angle and chord problems\n## Tangents, diameters, and central angles\n## Proofs using circle theorems","[{\"question\":\"How do you find an angle like ACD or ADC in these circle theorems questions?\",\"answer\":\"Identify the relevant theorem based on whether the given angle is central, angles formed with tangents, or angles in triangles. Then use known angle relationships such as supplementary angles and triangle angle sums.\"},{\"question\":\"What role do diameters and tangents play in the calculations?\",\"answer\":\"Diameters often help establish right angles with tangents or enable straightforward angle properties. Tangents are used to connect angles between a tangent and a radius/chord to angles in the opposite segment.\"},{\"question\":\"How are proof questions like proving angle ROS = 2x approached?\",\"answer\":\"Break the diagram into steps, establish intermediate angles using circle theorems, and use angle-chasing with justified reasons for each stage to reach the required relationship.\"}]","Circle Theorems Practice Questions - Angle Problems | PDF",1788601119,28,{"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-practice-questions-angle-problems","",{"@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-practice-questions-angle-problems/207781/",{"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","2026-09-08","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},"How do you find an angle like ACD or ADC in these circle theorems questions?","Question",{"text":75,"@type":76},"Identify the relevant theorem based on whether the given angle is central, angles formed with tangents, or angles in triangles. Then use known angle relationships such as supplementary angles and triangle angle sums.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What role do diameters and tangents play in the calculations?",{"text":80,"@type":76},"Diameters often help establish right angles with tangents or enable straightforward angle properties. Tangents are used to connect angles between a tangent and a radius/chord to angles in the opposite segment.",{"name":82,"@type":73,"acceptedAnswer":83},"How are proof questions like proving angle ROS = 2x approached?",{"text":84,"@type":76},"Break the diagram into steps, establish intermediate angles using circle theorems, and use angle-chasing with justified reasons for each stage to reach the required relationship.","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},[93,97,101,104,109,114,119,124,129,132,136],{"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":120,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":122,"slug":123},8,"Research & Report",30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":105,"slug":139},19,"General","general"]