# Metric Relationships in A Circle

## Metric Relationships in A Circle

Relationships between the measures of various segments formed by the intersection of a circle and two secants to the circle.

### Properties

$$\dfrac{\textrm{m}{\overline {\textrm{AX}}}}{\textrm{m}{\overline {\textrm{CX}}}}$$ = $$\dfrac{\textrm{m}{\overline {\textrm{DX}}}}{\textrm{m}{\overline {\textrm{BX}}}}$$

$$\dfrac{\textrm{m}{\overline {\textrm{AX}}}}{\textrm{m}{\overline {\textrm{XT}}}}$$ = $$\dfrac{\textrm{m}{\overline {\textrm{XT}}}}{\textrm{m}{\overline {\textrm{BX}}}}$$

$$\textrm{m}\overline {\textrm{AX}} \times \textrm{m}\overline {\textrm{XB}}$$ = $$\textrm{m}\overline {\textrm{CX}} \times \textrm{m}\overline {\textrm{XD}}$$

$$\textrm{m}\overline {\textrm{CX}}$$ = $$\textrm{m}\overline {\textrm{XD}}$$ = $$\sqrt{\textrm{m}{\overline {\textrm{AX}}} \times \textrm{m}{\overline {\textrm{XB}}}}$$

$$\textrm{m}\overline {\textrm{AB}} \times \textrm{m}\overline {\textrm{CD}}$$ + $$\textrm{m}\overline {\textrm{BC}} \times \textrm{m}\overline {\textrm{DS}}$$ = $$\textrm{m}\overline {\textrm{CX}} \times \textrm{m}\overline {\textrm{CX}}$$