Circle Theorems Calculator

Your details

Choose the circle theorem you want to apply. Each mode shows only the relevant inputs.
The angle at the centre of the circle subtended by the same arc. The inscribed angle is half this value.
deg
The radius of the circle. Used to calculate arc length.
units
ResultInscribed angle = central angle / 2
40

Main computed value for the selected theorem

Secondary result6.9813
Primary output nameInscribed angle (deg)
Secondary output nameArc length (same units as radius)

Inscribed angle is 40.00 deg (half of central angle 80 deg).

  • An inscribed angle is always exactly half the central angle that subtends the same arc.
  • The arc intercepted by the central angle (80 deg) has length 6.9813 units for a radius of 5 units.
  • If you move the vertex of the inscribed angle to any other point on the same arc, the angle stays the same.

Next stepTry the Thales Theorem mode to see how the inscribed angle theorem produces a 90-degree angle whenever the chord is the diameter.

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