# Angles Outside a Circle

## Basic Concept

#### Angles Outside a Circle

$$\beta = \dfrac{\text{m}\overset {\huge\frown} {\text{AC}} - \text{m}\overset {\huge\frown} {\text{DF}} }{2}$$

$$\text{m}\angle \text{ABC} = \dfrac{\text{m}\angle \text{AOC} - \text{m}\angle \text{FOD}}{2}$$

$$\alpha = \dfrac{\text{m}\overset {\huge\frown} {\text{AC}} + \text{m}\overset {\huge\frown} {\text{DF}} }{2}$$

$$\text{m}\angle \text{DEF} = \dfrac{\text{m}\angle \text{AOC} + \text{m}\angle \text{FOD}}{2}$$

#### Segments From Secants

If two secants are drawn from a common point outside a circle then $$\:\color{blue} a(a + b) = c(c + d)$$