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I'm Up and Down, and Round and Round

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A circle looks plain. It holds thirteen separate rules.

One circle, four named parts.

This is Chapter 5. It is called I'm Up and Down, and Round and Round. This track covers its main ideas.

What you will learn

  • The four parts — chord, arc, segment, sector.
  • Chord and centre — a 90° line from the centre halves the chord.
  • Equal chords — in one circle, same distance from the centre, same length.
  • Twice as big — centre angle is double the edge angle, same arc.
  • The same segment — one arc, one fixed angle, everywhere on it.
  • A half circle — a diameter gives a right angle at the rim.
  • Four on one circle — opposite angles of the four-sided shape total 180°.
  • Are they concyclic? — a test for four points on one circle.
  • Three points, one circle — two lines cross at the centre.
  • Two points — endless circles pass through them; centres lie on one line.
  • Turning and flipping — a circle looks the same after any turn.
  • Equal angles, equal chords — the chord rules, in the other direction.
  • Equal angles on one side — four points lie on one circle.

Need a quick recap?

These earlier lessons help. Tap one if you are unsure.

  • What a circle is — every point the same distance from the centre.
  • Measuring an angle — degrees, read on a protractor.
  • The angle that leans out — it equals the two far corners added.
  • Longest side, widest corner — and two equal sides give two equal corners.
  • Finding a shorter side — subtract squares, then take the root.
  • The four angles come to 360° — true of any four-sided shape.

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This track

  1. 0 Start here
  2. 1 Four names for four parts of a circle
  3. 2 The line from the centre that cuts a chord in half
  4. 3 Same distance, same length — and further out is shorter
  5. 4 An arc makes twice the angle at the centre that it makes at the edge
  6. 5 Every point on one arc sees the chord the same way
  7. 6 Checkpoint: parts, chords and the doubling
  8. 7 A corner standing on a diameter is a right angle
  9. 8 Four corners on one circle, and the pairs that total 180°
  10. 9 Testing whether four points really share one circle
  11. 10 Three points give one circle, and the triangle shows where its centre is
  12. 11 Checkpoint: diameters, cyclic shapes and finding a centre
  13. 12 Many circles fit through two points
  14. 13 A circle looks the same when turned
  15. 14 Equal angles at the centre give equal chords
  16. 15 Equal angles on one side put four points on a circle
  17. 16 The big picture
  18. 17 Track quiz

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