The Diminished Chord, Changing the Melody or the Chords, Common Tones, Pedal Points
Symmetry in Circles (II) Chords A chord is a line connecting any two points on the circumference....
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Symmetry in Circles (II) Chord s A chord is a line connecting any two points on the circumference. chor d The biggest possible chord is the diamet er
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Transcript of Symmetry in Circles (II) Chords A chord is a line connecting any two points on the circumference....
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
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.
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Ex1
A B
x
y
Radius = 15cm and AB = 24cm.
Find x & y.
**********
1212
15x
By Pythagoras
x2 = 152 - 122
x2 = 225 - 144
x2 = 81
x = 81x = 9cm
y = 15 - 9
y = 6cm
y
Ex2
A B
x
Radius = 34cm and x = 16cm .
Find AB.
**********
3416
By Pythagoras
y2 = 342 - 162
y2 = 1156 - 256
y2 = 900
y = 900y = 30
AB = 2 X 30
AB = 60cm
yA B
Ex3 A tunnel of radius 8m has a road of width 10m running through it.
Find the height of the tunnel.
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8
8
5
x
By Pythagoras
x2 = 82 - 52
x2 = 64 - 25
x2 = 39
x = 39
x = 6.24
Height = 8 + 6.24
= 14.24m
Ex4In a pipe of diameter 50cm the surface of the water is 18cm wide
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18cm
How deep is the water?
25
25
9
x
By Pythagoras
x2 = 252 - 92
x2 = 625 - 81
x2 = 544
x = 544
x = 23.3
Depth = 25 + 23.3
= 48.3cm
