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Mathematics
Central and inscribed angles
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Drag points around a circle with centre O to compare central angles, inscribed angles and intercepted arcs.
Move C
Point covered? Select it here, then use the two move buttons above the circle.
Keyboard controls
Arrow keys: move 1°. Page Up/Down: 10°. Home/End: positions 0°/359°. Escape: cancel dragging.
- Arc AB not containing C
- 120°
- Minor arc
- Inscribed angle ∠ACB
- β = 60°
- Central angle ∠AOB
- α = 120°
Relationship
β = α / 2
Keep A and B fixed and move C along the same arc: angle β stays constant.
Computed from geometry · ≈ marks rounding
Why it works
Separate proof diagram; independent of the draggable figure.
Extend CO to D on the circle. Rays OC and OD are opposite, so CD is a diameter.
Model notes
- The model uses an ideal circle and points in a Euclidean plane. A, B, C and D stay on the same circle; the display size does not affect the angles.
- The central angle α is at most 180°. An inscribed angle is half the measure of the arc AB that does not contain its vertex. For a major arc, use (360° − α)/2 instead of α/2.
- Measurements are computed from geometry rather than measured with a protractor. The ≈ sign marks rounding. A vertex at an endpoint, or coincident A and B, makes the corresponding values undefined, shown as —. Select and separate the points to continue.
- Exploring many configurations reveals a pattern but does not replace a proof. Why it works illustrates reasoning with an isosceles triangle and an exterior angle in the diameter case.