Inscribed Angle

Inscribed Angle

An angle whose vertex is on a circle and whose sides are chords of the circle.


The degree measure of an inscribed angle is equal to one-half of the degree measure of the arc intercepted by the sides of the angle.


  • In the figure below, angle BAC is an angle inscribed in the circle with centre O.

  • \(m∠\textrm{BAC} = \frac{\textrm{m} {\widehat{\textrm{BC}}}}{2}\)

    \(m∠\textrm{BAC} = \frac{60}{2}= 30\)

  • The degree measure of an angle inscribed in a semicircle is equal to that of a right angle.

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