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Inscribed Angle Theorem Calculator

Online inscribed angle calculator. Enter the central angle over the same arc to find the inscribed angle (half the central angle), with the theorem—great for circle geometry.

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Inscribed angle = half the central angle over the same arc
Central angle over the same arc

📖 Tutorial | Inscribed Angle

1. Definition
An inscribed angle has its vertex on the circle and sides meeting it.
2. Formula & Notation
cCentral angle
c/2Inscribed angle
3. Properties & Laws
  • Half the central angle;
  • Angles over the same arc equal;
  • Over a diameter it is 90°;
  • Cyclic quadrilateral opposite angles supplementary.
4. Steps
  1. Enter central angle c;
  2. Click "Find";
  3. Or click "Load Example".
5. Worked Examples
Example: central 80°.
Solution: inscribed = 40°.
6. Common Pitfalls
Use the same arc;
Diameter gives 90°;
Vertex must be on the circle.

❓ FAQ | Inscribed Angle

The theorem?
Half the central angle over the same arc.
Over a diameter?
90°.
Central 80?
40°.
Same arc angles?
Equal.
Cyclic quadrilateral?
Opposite angles supplementary.
Chord for 90°?
Diameter.