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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.

Example

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

Property

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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