1. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty1 Isosceles Triangles in Circles Right angle in a Semi-Circle The Circle www.mathsrevision.com Tangent Line to a Circle Diameter Symmetry in a Circle Circumference of a Circle Length of an ARC of a Circle Area of a Circle Area of a SECTOR of a Circle Summary of Circle Chapter

2. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty2 When two radii are drawn to the ends of a chord, An isosceles triangle is formed. C A B www.mathsrevision.com Isosceles triangles in Circles

3. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty3 Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180 o www.mathsrevision.com Isosceles triangles in Circles

4. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty4 Q.Find the angle x o. A B C Solution Angle at C is equal to: Since the triangle is isosceles we have xoxo 280 o www.mathsrevision.com Isosceles triangles in Circles

5. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty5 Tangent line A tangent line is a line that touches a circle at only one point. Which of the lines are tangent to the circle? www.mathsrevision.com

6. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty6 Tangent line The radius of the circle that touches the tangent line is called the point of contact radius. Special Property The point of contact radius is always perpendicular (right-angled) to the tangent line. www.mathsrevision.com

7. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty7 Tangent line Q.Find the length of the tangent line between A and B. A and B. A B 8 10 C Solution Right-angled at A since AC is the radius at the point of contact with the Tangent. By Pythagoras Theorem we have www.mathsrevision.com

8. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty8 Diameter symmetry AB C D 1.A line drawn through the centre of a circle through the midpoint a chord will ALWAYS cut the chord at right-angles 2.A line drawn through the centre of a circle at right-angles to a chord will ALWAYS bisect that chord. 3.A line bisecting a chord at right angles will ALWAYS pass through the centre of a circle. O

9. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty9 Q.Find the length of the chord A and B. A B 6 O Solution By Pythagoras Theorem we have Diameter symmetry 4 Since yellow line bisect AB and passes through centre O, triangle is right-angle. Radius of the circle is 4 + 6 = 10. 10 Since AB is bisected The length of AB is www.mathsrevision.com

10. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty10 Main parts of the circle radius O Circumference Diameter www.mathsrevision.com Circumference of a circle

11. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty11 Q.Find the circumference of the circle ?Solution 4cm www.mathsrevision.com Circumference of a circle

12. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty12 Q. The circumference of the circle is 60cm ? Find the length of the diameter and radius.Solution www.mathsrevision.com Circumference of a circle

13. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty13 Q. What is an arc ? A B Answer An arc is a fraction of the circumference. minor arc major arc www.mathsrevision.com length of the arc of a circle

14. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty14 Q. Find the circumference of the circle ?Solution 10cm www.mathsrevision.com length of the arc of a circle

15. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty15 Q. Find the arc length for the semi-circle ? Solution 180 o www.mathsrevision.com length of the arc of a circle

16. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty16 Q. Given part of the circle below. Find the arc length ? Solution 10cm 90 o www.mathsrevision.com length of the arc of a circle

17. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty17 3 step process to calculating the length of an arc. Step 1 Find the circumference of the circle. Step 2 Find fraction of the whole circle. Step 3 Find the arc length. www.mathsrevision.com length of the arc of a circle

18. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty18 Solution 6cm 45 o Q. Part of a circle is given below. Find the arc length. Fraction of circle www.mathsrevision.com length of the arc of a circle

19. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty19 3 step process to calculating the length of an arc. Step 1 Find the circumference of the circle. Step 2 Find fraction of the whole circle. Step 3 Find the arc length. www.mathsrevision.com length of the arc of a circle

20. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty20 Q. Find the length of the arc AB below ? 9 cm 60 o A BSolution www.mathsrevision.com length of the arc of a circle

21. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty21 Q. The diameter of the circle is 60cm. Find area of the circle?Solution www.mathsrevision.com The Area of a circle

22. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty22 Q. The area of a circle is 12.64 cm 2. Find its radius?Solution www.mathsrevision.com The Area of a circle

23. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty23 Q. What is an sector area ? Sector area of a circle A B Answer Sector area is a fraction of the area of the whole circle. minor sector major sector www.mathsrevision.com

24. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty24 Sector area of a circle Q. Find the area of the circle ?Solution 10cm www.mathsrevision.com

25. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty25 Q. Find the sector area for the semi-circle ? Solution Sector area of a circle 180 o 10cm www.mathsrevision.com

26. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty26 Q. Given part of the circle below. Find the sector area ? Solution Sector area of a circle www.mathsrevision.com

27. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty27 Sector area of a circle 3 step process to calculating sector area of a circle. Step 1 Find the area of the circle. Step 2 Find fraction of the whole circle. Step 3 Find the sector area. www.mathsrevision.com

28. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty28 Solution 6cm Sector area of a circle 45 o Q. Part of a circle is given below. Find the sector area. Fraction of circle www.mathsrevision.com

29. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty29 Sector area of a circle 3 step process for calculating the sector area. Step 1 Find the area of the circle. Step 2 Find fraction of the whole circle. Step 3 Find the sector area. www.mathsrevision.com

30. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty30 Q. Find the area of the sector below ? Sector area of a circle Solution www.mathsrevision.com

31. S3 Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Friday, 17 April 2015Created by Mr Lafferty31 Area is Summary of Circle Topic Circumference is Sector area Arc length is Diamete r Radius line that bisects a chord 1.Splits the chord into 2 equal halves. 2.Makes right-angle with the chord. 3.Passes through centre of the circle Pythagoras Theorem SOHCAHTOA Semi-circle angle is always 90 o Tangent touches circle at one point and make angle 90 o with point of contact radius www.mathsrevision.com