Every point on one arc sees the chord the same way

Hold a chord still. Slide a corner point along its own arc.

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.

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?

Try the lab to finish this lesson.