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

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. ||

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

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

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

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 = x 2 = x 2 = 544 x =  544 x = 23.3 Depth = = 48.3cm