Exterior Angle of a Circle

Exterior Angle of a Circle

Angle whose vertex is outside a circle and whose sides are tangents or secants to the circle.


In the figure below, angle BAE is an exterior angle of the circle with centre O.


The degree measure of angle BAC below is equal to one-half the difference of the degree measures of the arcs intercepted by the sides of the angle.

m\(\angle{\textrm{BAC}} = \frac{\textrm{m} \widehat{\textrm{DE}} – \textrm{m}\widehat{\textrm{BC}}}{2}\)

m\(\angle{\textrm{BAC}} = \frac{90 – 50}{2}=\frac{40}{2}=20\)

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