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A circle looks plain. It holds thirteen separate rules.

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.