Every point on one arc sees the chord the same way
Hold a chord still. Slide a corner point along its own arc.
Step 1 of 4
- Chord AB, and the arc left over.
- Point P on that arc, angle APB drawn.
- Point Q, elsewhere on the same arc.
- Angle AQB, equal to angle APB.
The rule
A point reads the angle between its lines to A and B.
Fix a chord AB that is not a diameter. That fixes the angle at the centre O on the minor arc. Every point P on the major arc reads half of that angle. Half of a fixed number is also a fixed number. So every point on that arc reads the same angle.
In the same segment — on one arc of the same chord. Angles in the same segment are equal.
Two arcs, two readings
Take a chord whose minor arc holds 100° at the centre.
- Every point on the major arc reads 100° ÷ 2 = 50°.
- Every point on the minor arc reads 260° ÷ 2 = 130°.
The 260° is 360° − 100°, the long way round the centre.
| Point | Its arc | Angle it reads |
|---|---|---|
| P | major | 50° |
| Q | major | 50° |
| R | major | 50° |
| S | minor | 130° |
| T | minor | 130° |
Which arc a point sits on decides its angle. Where it sits along that arc does not matter.
P reads one number. What does Q read?
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