# 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$$\angle{\textrm{BAC}} = \frac{90 – 50}{2}=\frac{40}{2}=20$$