Symmetry in Circles (II)

1
Symmetry in Circles (II)
Chords
A chord is a line connecting any two points on
the circumference.
chord
The biggest possible chord is the
diameter
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
Radius 15cm and AB 24cm.
Find x y.
x
A
B
y

By Pythagoras
x2 152 - 122
y 15 - 9
x2 225 - 144
y 6cm
15
x
x2 81
12
x ?81
12
y
x 9cm
4
Ex2
Radius 34cm and x 16cm .
Find AB.
x
A
B

By Pythagoras
y2 342 - 162
AB 2 X 30
y2 1156 - 256
AB 60cm
34
16
y2 900
A
y ?900
B
y
y 30
5
Ex3
A tunnel of radius 8m has a road of width 10m
running through it.
Find the height of the tunnel.

By Pythagoras
Height 8 6.24
x2 82 - 52
8
14.24m
x2 64 - 25
8
x
x2 39
5
x ?39
x 6.24
6
Ex4
In a pipe of diameter 50cm the surface of the
water is 18cm wide
18cm
How deep is the water?

By Pythagoras
9
x2 252 - 92
Depth 25 23.3
x
25
x2 625 - 81
48.3cm
x2 544
25
x ?544
x 23.3