1. Symmetry in Circles (II) Chords A chord is a line connecting any two points on the circumference. chord The biggest possible chord is thediameter

2. Chords & Radii When a radius is drawn through the middle of a chord the angle formed is 90°. Drawing in additional radii gives us right-angled triangles and we can then use Pythagoras calculations. ||

3. Ex1 AB x y Radius = 15cm and AB = 24cm. Find x & y. ********** 12 15 x By Pythagoras x 2 = 15 2 - 12 2 x 2 = 225 - 144 x 2 = 81 x =  81 x = 9cm y = 15 - 9 y = 6cm y

4. Ex2 AB x Radius = 34cm and x = 16cm. Find AB. ********** 34 16 By Pythagoras y 2 = 34 2 - 16 2 y 2 = 1156 - 256 y 2 = 900 y =  900 y = 30 AB = 2 X 30 AB = 60cm y A B

5. Ex3 A tunnel of radius 8m has a road of width 10m running through it. Find the height of the tunnel. ************* 8 8 5 x By Pythagoras x 2 = 8 2 - 5 2 x 2 = 64 - 25 x 2 = 39 x =  39 x = 6.24 Height = 8 + 6.24 = 14.24m

6. Ex4 In a pipe of diameter 50cm the surface of the water is 18cm wide ********** 18cm How deep is the water? 25 9 x By Pythagoras x 2 = 25 2 - 9 2 x 2 = 625 - 81 x 2 = 544 x =  544 x = 23.3 Depth = 25 + 23.3 = 48.3cm