Read each question carefully before you begin answering it. A collection of 91 maths gcse sample and specimen questions from aqa, ocr, pearsonedexcel and wjec eduqas. Let s be the point on pq, not t, such that osp is a right angle. Write down the name of the circle theorem used in part b. The theorems pyramid peaks from this angle is half the angle in the centre speedo logo the same two points are equal a triangle made from a diameter touches the circumference at 90o when a four sided shape touches the circumference of a circle at all corners, opposite interior angles add to 180o. Learn about and revise the different angle properties of circles described by different circle theorems with gcse bitesize aqa maths.
Gcse mathematics non calculator paper 10 practice paper style questions topic. Circle theorems higher circle theorems bbc bitesize. These are not circle theorems, but are useful in questions involving circle theorems. Circle theorems maths revision circle theorems, gcse. Calculate the size of the following angles, giving a geometrical reason for each of your answers. Type your answers into the boxes provided leaving no spaces. Give a reason for each stage in your working total for question 7 is 5 marks. Proving circle theorems angle in a semicircle we want to prove that the angle subtended at the circumference by a semicircle is a right angle. Angle between tangent and radius is 90 3 angle abc 67. The smaller of 2 angles when a circle is split into 2 uneven parts. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
The video below highlights the rules you need to remember to work out circle theorems. On your igcse gcse maths exam you will not only have to calculate angles in polygons, you will also have to be able to find angles in circles. Fourth circle theorem angles in a cyclic quadlateral. Angle ado 38 a work out the size of angle aod 2 b i work out the size of angle abc ii give a reason for your answer. Our circle theorems tell us that the angle in a semicircle is a rightangle so bad must be 9 0 90\degree 9 0. This section explains circle theorem, including tangents, sectors, angles and proofs. Gcse 91 exam question practice circle theorems teaching. Diagram not drawn to scale calculate the size of pqr in terms of x. Past paper exam questions organised by topic for edexcel gcse maths. Straight away then move to my video on circle theorems 2 exam questions 14. Circle theroms maths questions worksheets and revision mme. Pencil, pen, ruler, protractor, pair of compasses and eraser. Mathematics non calculator paper 10 practice paper style questions topic. Aqa, ocr, edexcel gcse maths circle theorems questions name.
Angle at centre is twice angle at circumference 4 angle abc 92 reason. Slides in pdf one slide per page, suitable for importing into iwb software. You will use results that were established in earlier grades to prove the circle relationships, this. Gcse maths circle theorems educational poster size. Circle theorems h gcse maths tutorials, revision and. Firstly, recognise that since bd is a diameter, angle bad is the angle in a semicircle. Circle theorems higher tier for this paper you must have. What are circle theorems help with igcse gcse maths. Max actual rag 1 4 2 4 3 4 4 4 5 4 6 4 7 2 8 5 9 4. First circle theorem angles at the centre and at the circumference. Many students are intimidated by the circle theorems and think they are difficult to. More lessons for gcse maths math worksheets examples, solutions, and videos to help gcse maths students learn the circle theorems.
Circle theorems objectives to establish the following results and use them to prove further properties and solve problems. Mathematics linear 1ma0 circle theorems materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres, protractor, compasses, pen, hb pencil, eraser. Year 11 circle theorems question sheets and mark scheme. The angle subtended at the circumference is half the angle at the centre subtended by the same arc angles in the same segment of a circle are equal a tangent to a circle is perpendicular to the radius drawn from the point. The line pqr is a tangent to a circle with centre o.
The angle between a radius and a tangent is 90 degrees. Circle theorems for cie igcse mathematics geogebra. Dfm is a huge bank of free educational resources for teaching mathematics, with full sets of slides, worksheets, games and assessments that span year 7 to further maths and enrichment resources with a maths challengeolympiad focus. Sep 06, 2012 introduction to circles, radii, diameters, sectors, arcs, segments, chords, and the seven circle theorems. Abcd is a cyclic quadrilateral within a circle centre o. The other two sides should meet at a vertex somewhere on the. Angles subtended by an arc in the same segment of a circle are equal. In short, the red angles are equal to each other and the green angles are equal to each other. Geometry formulas math formulas circle math circle geometry circle theorems gcse maths revision revision notes math charts math notes. The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment. Slides in pdf one slide per page, suitable for importing into iwb software worksheet. L a chord of a circle is a line that connects two points on a circle.
Once we draw some lines inside a circle, we can deduce patterns and theorems that are useful both theoretically and in a practical sense. Points a, b and c are all on the circumference of the circle. The two tangents drawn to a circle from a point are equal in length. Circle theorems h a collection of 91 maths gcse sample and specimen questions from aqa, ocr, pearsonedexcel and wjec eduqas. Maths revision video and notes on the topic of circle theorems. Line a b is a straight line going through the centre o. Worksheets galore this is from the castleford academy and has lots of links for worksheets sorted by grade and subject and all downloadable pdf. This is my poster for circle theorems, which provides a great reference for the main theorems. The opposite angles in a cyclic quadrilateral add up to 180 degrees the. In the diagram below, o is the centre of the circle and a, b and c are points. I give students the a5 version for revision and have a large version on the wall somewhere.
Perhaps one day try a random topic and discover new maths activities and example questions. Firstly, recognise that since bd is a diameter, angle bad is the angle in a semi circle. Circle theorems higher circles have different angle properties described by different circle theorems. The angle at the circumference is half the angle at the centre. If you like this resource, then please rate it andor leave a comment if the rateresource button on this page does not work, then go to. More information on circles can be found on the circle theorems page here. B, d and e are points on the circumference of a circle, centre o.
Igcse mathematics practice worksheet circle theorem worksheet 14 student name. Give a reason from your answer b work out the size of angle deb. Thus, the diameter of a circle is twice as long as the radius. Circle theorems topic questions edexcel gcse maths. I also make them available for a student who wants to do focused independent study on a topic. Circle theorems gcse higher ks4 with answerssolutions. Pencil, pen, ruler, protractor, pair of compasses and eraser you may use tracing paper if needed guidance 1. Geometry formulas math formulas circle math circle geometry circle theorems gcse maths revision revision. Aug 22, 2017 this is a unit of work that i have created on circle theorems for gcse higher maths consisting of 6 lessons covering all circle theorems.
Maths made easy complete tuition ltd 2017 circle theorems 1. The perpendicular from the centre of a circle to a chord will always bisect the chord split it into two equal lengths. Sixth circle theorem angle between circle tangent and radius. The angle at the centre is twice the angle at the circumference. Math geometry formula pdf geometry math formula in hindi pdf. L the distance across a circle through the centre is called the diameter. Opposite angles in a cyclic quadrilateral sum to 180. Angle subtended at the centre of a circle is twice the angle at the circumference. This page will show you all the maths topics discussed on. Investigations on circle theorems for cie igcse mathematics. If you click on it, you will immediately be directed to the appropriate page.
Gcse maths circle theorems educational poster size a2. Circle theorems free maths worksheets and other resources one of my favourite parts of maths to teach, great for letting pupils investigate and discover circle theorems for themselves. A, b and c are points on the circumference of a circle, centre o. Full examples and questions for complete specification. This video is for students attempting the higher paper aqa unit 3 maths gcse, who have previously sat the foundation. Circle theorems gcse higher ks4 with answerssolutions note. The angle between a tangent and a radius at the point of contact is a right angle.
Create the problem draw a circle, mark its centre and draw a diameter through the centre. Edexcel gcse mathematics linear 1ma0 circle theorems materials required for examination items included with question papers ruler graduated in centimetres and nil millimetres, protractor, compasses, pen, hb pencil, eraser. Pdf circle theorems gcse higher ks4 with answerssolutions circle theorems gcse higher ks4 with answerssolutions note. Mar 20, 2014 year 11 circle theorems question sheets and mark scheme. Lots of questions and examples at grades 7, 8 and 9. You can earn a trophy if you get at least 7 questions correct. Mathematics linear 1ma0 circle theorems maths genie. Points a, b and c are all on the circumference of the circle, o represents. This section will explain the various circle theorems to you. Our circle theorems tell us that the angle in a semi circle is a rightangle so bad must be 9 0 90\degree 9 0. Therefore ot os as ot is the hypotenuse of triangle ots. Angles in a semicircle angle at the centre double the angle at the circumference angles from the same chord in the same segment. I usually print these questions as an a5 booklet and issue them in class or give them out as a homework.
This video looks at gcse higher tier circle theorems and covers. Angle subtended at the centre of a circle is twice the angle subtended at the circumference. The points p, q and r lie on the circumference of a circle, centre o. In my opinion, the most important shape in maths is the circle. Jun 02, 2012 straight away then move to my video on circle theorems 2 exam questions 14. Gcse maths revision circle theorems questions maths made easy. You must give a reason for each step of your solution. We are working hard on a new platform for setting, building and monitoring homework. Circle theorems are used in geometric proofs and to calculate angles. I give students the a5 version for revision and have a.
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