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Symmetry in Circles (II)

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 °. |. |.

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Symmetry in Circles (II)

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  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 y 12 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 B y = 900 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

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