5. The radius of a circle is given in each of the following. Use it to fi nd the diameter. (i) 22 cm


(ii) 16 mm (ii) 36 mm (iii) 65 m (iii) 15 m (iv) 8 ⋅ 4 km


6. The diameter of a circle is given in each of the following. Use it to fi nd the radius. (i) 12 cm


7. Use the circle to name the coordinates of the following points. (i) Centre (ii) Endpoints of any diameter (iii) Endpoints of any chord that is not a diameter (iv) Endpoints of any radius


(iv) 17 ⋅ 4 km y


(v) 9 ⋅ 6 cm (v) 7 ⋅ 5 cm


1 1


8. The diagram shows a blue circle with centre A and a red circle with centre B .


(i) What are the coordinates of A ? (ii) What are the coordinates of B ? (iii) What word could you use to describe [AB] ?


(iv) Write down the coordinates of the endpoints of the vertical diameter of the blue circle.


(v) Write down the coordinates of the endpoints of the horizontal diameter of the blue circle.


20.2 Circle theorem and corollaries


We can also say that it stands on the chord [BC]. 1 1 x y x


A B


By the end of this section you should be able to: ● understand the circle theorem (Theorem 19) and its corollaries ● apply the circle theorem (Theorem 19) and its corollaries


B and C are the ends of an arc of a circle and A is another point on the circle, which is not on the arc. We can say that the angle ∠BAC is the angle at the point A on the circle, standing on the arc BC .


B Chord Arc C Discuss and discover


Work with a classmate to complete the following tasks. (i) Using a compass, draw a circle and mark the centre, O . (ii) Mark out an arc on your circle and label the ends of the arc B and C . (iii) Mark a point, A, anywhere on the circle. (iv) Using a protractor, measure | ∠BOC | and | ∠BAC |. (v) Compare the measurements of the angles. What do you notice? (vi) Repeat the above steps for two more circles.


330 Linking Thinking 2


A


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