The third activity contains a miscellany of probing questions which can be used in a variety of ways in the classroom in order to assess student understanding. In this exercise students are required to complete the square to rearrange the equation of the circle into a form that can be used to determine whether the statement is true or false. Find the perpendicular distance from the centre of the circle to this chord. Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. At the more straightforward or superficial level, we have to know formulae, learn to recognise the. Once again students are required to justify their answer showing the mathematics they have used. (3 marks) (3 marks) (a) (b) (c) Find: (i) the coordinates of the centre of the circle (ii) the radius of the circle in the form pv', where p is an integer. OA 2 AB 2 + OB 2 (by Pythagoras Theorem) 5 2 4 2 + OB 2. Questions on The Circle generally occur at two levels. The second activity asks students to determine whether each of a number of statements is true or false. 11 learners academic achievement in South Africa. Where necessary, give your answer as a surd in its simplest form. In Maths or Geometry, a circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. This paper reports the use of GeoGebra software in teaching and learning circle geometry enhancing Grade. A video revising the techniques and strategies required for all of the AS Level Pure Mathematics chapter on Circles that you need to achieve a grade C-A in. For each circle, work out the radius and the coordinates of the centre. There is not a unique solution to this problem thus requiring students to explain the mathematics used to justify their solution. Write down the coordinates of the centre and the radius of each circle. The first activity requires students to match the equations of circles to statements cards. When you move point 'B', what happens to the angle Inscribed Angle Theorems. Each activity is accompanied by teacher notes suggesting how the activity could be delivered and possible extension ideas. Three advanced level lesson ideas from Susan Wall designed to explore the properties of circles and their equations. a = 2b.Quality Assured Category: Mathematics Publisher: Susan Wall The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. But x + y is the size of the angle we wanted to find.Ī tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).Ī tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent.Īlso, if two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same. ![]() Sheet 1 (From OCR) Sheet 2 (From Edexcel) Related Tutoral Video. Therefore x + y + x + y = 180, in other words 2(x + y) = 180.Īnd so x + y = 90. (3 marks) (3 marks) (a) (b) (c) Find: (i) the coordinates of the centre of the circle (ii) the radius of the circle in the form pvî, where p is an integer. Although the following questions are predominantly from the OCR, OCR MEI and Edexcel exam boards, they are suitable practice for all UK A Level Maths qualifications unless otherwise stated. Therefore each of the two triangles is isosceles and has a pair of equal angles.īut all of these angles together must add up to 180°, since they are the angles of the original big triangle. ![]() Calculate the length of the line BC correct to 1 1 decimal place. The equation of a circle centred at the origin The simplest case is that of a circle whose centre is at the origin. The line AE is 5cm 5cm and angle ADE 71o 71o. The chord AB is perpendicular to the line CD at the point E. Points A, B, C, and D are on the circumference of the circle. Exercise: Find the area of circular sector in ‘m 2 ’, that has perimeter of 100 cm with arc length of 40 cm. Example 5: chord of a circle (cosine ratio) Below is a circle with centre C. Sacred geometry is a concept developed in ancient times grounded on the idea that the world is created based on a consistent geometrical pattern. Using the formula, we have Area lawn 0.5 x (10) 2 x /2 78.54 m 2. We know that each of the lines which is a radius of the circle (the green lines) are the same length. We are required to find the area of a grass lawn in ‘m 2 ‘ that has side length of 10 m and a subtended angle of /2. We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches.
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