Mathematics Class 9
I'm Up and Down, and Round and Round
Chords, the centre-angle rule, cyclic shapes, circle symmetry, and circles through points.
18 lessons · ~140 min total
Track progress — 0 of 18 lessons read 0%
Lessons in this topic
- 0 Start here A roadmap: chords, the centre, the doubling angle, cyclic shapes, symmetry, and circles through points. · 3 min You are here
- 1 Four names for four parts of a circle Chord, arc, segment and sector — the four words this whole chapter is built from. · 7 min
- 2 The line from the centre that cuts a chord in half The 90° line from the centre meets a chord, not a diameter, at its middle. · 9 min
- 3 Same distance, same length — and further out is shorter Two chords the same distance from the centre match in length. Further out is always shorter. · 8 min
- 4 An arc makes twice the angle at the centre that it makes at the edge The angle an arc holds at the centre is double the angle it holds at the rim. · 10 min
- 5 Every point on one arc sees the chord the same way Slide the corner point anywhere along its own arc. The angle it makes does not change. · 8 min
- 6 Checkpoint: parts, chords and the doubling A graded check on the first five ideas — the four names, chord distance, and the doubling angle. · 6 min
- 7 A corner standing on a diameter is a right angle Join both ends of a diameter to any point on the circle. That corner is exactly 90°. · 8 min
- 8 Four corners on one circle, and the pairs that total 180° When all four corners sit on one circle, each pair of opposite angles adds to exactly 180°. · 9 min
- 9 Testing whether four points really share one circle Three points not in a line always share a circle. Four points only sometimes do. · 9 min
- 10 Three points give one circle, and the triangle shows where its centre is Two perpendicular bisectors cross at the centre of the circle through all three points. · 10 min
- 11 Checkpoint: diameters, cyclic shapes and finding a centre A graded check on the second half — the right angle on a diameter, cyclic angles, and the circumcentre. · 6 min
- 12 Many circles fit through two points The centres of all circles through two points lie on one line. · 8 min
- 13 A circle looks the same when turned A circle fits itself after any turn. Every diameter is a mirror line. · 7 min
- 14 Equal angles at the centre give equal chords Equal angles at the centre give equal chords in one circle. · 8 min
- 15 Equal angles on one side put four points on a circle Equal angles on one side put four points on one circle. · 9 min
- 16 The big picture Thirteen ideas about circles, tied back together around one point: the centre. · 6 min
- 17 Track quiz Cheat-sheet table plus a reveal quiz — one question for each of the thirteen ideas. · 9 min
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