1. Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty1 Circles Revision of Angle Properties Angles in a semi-circle www.mathsrevision.com Pythagoras Theorem S4 SOHCAHTOA Tangent line on a circle

2. 25-Feb-16Created by Mr. Lafferty 120 o 95 o www.mathsrevision.com Angles round a point Add up to 360 o 115 o Two angles making a straight line add to 180 o angles opposite each other at a cross are equal. 34 o 3 angles in a triangle ALWAYS add up to 180 o. 50 o 40 o 65 o 90 o 146 o 146 o 145 o S4 Revision Angle Properties

3. 25-Feb-16Created by Mr. Lafferty www.mathsrevision.com Two angles in a isosceles Are equal ALL angles in an equilateral triangle are 60 o d = 115 o aoao coco bobo gogo fofo hoho eoeo is corresponding to d and must be 115 o is opposite to d and must be 115 o is must be 65 o (straight line) is alternate to c and must also be 65 o h b c e S4 Revision Angle Properties

4. Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty4 KeyPoint for Angles in a Semi-circle Angles in a Semi-Circle A triangle APB inscribed within a semicircle with hypotenuse equal to the diameter will ALWAYS be right angled at P on the circumference. Remember - Angles in any triangle sum to 180 o www.mathsrevision.com S4 P AB

5. Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty5 Hints www.mathsrevision.com Example 1 : Sketch diagram and find all the missing angles. 70 o Look for right angle triangles 43 o 20 o 47 o Remember ! Angles in any triangle sum to 180 o Angles in a Semi-Circle S4

6. Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty6 www.mathsrevision.com S4 Example 2 : Sketch the diagram. Angles in a Semi-Circle C AB D 25 o 60 o (a)Right down two right angle triangles (a)Calculate all missing angles. E

7. S4 Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty7 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 Angles in a Semi-Circle Tangent Line

8. S4 Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty8 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 Online Demo Angles in a Semi-Circle Tangent Line

9. S4 Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Thursday, 25 February 2016Created by Mr Lafferty9 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 Angles in a Semi-Circle Tangent Line