Relationships between the measures of various segments formed by the intersection of a circle and two secants to the circle.
Properties
\(\dfrac{\textrm{m}{\overline {\textrm{AX}}}}{\textrm{m}{\overline {\textrm{CX}}}}\) = \(\dfrac{\textrm{m}{\overline {\textrm{DX}}}}{\textrm{m}{\overline {\textrm{BX}}}}\)
\(\dfrac{\textrm{m}{\overline {\textrm{AX}}}}{\textrm{m}{\overline {\textrm{XT}}}}\) = \(\dfrac{\textrm{m}{\overline {\textrm{XT}}}}{\textrm{m}{\overline {\textrm{BX}}}}\)
\(\textrm{m}\overline {\textrm{AX}} \times \textrm{m}\overline {\textrm{XB}}\) = \(\textrm{m}\overline {\textrm{CX}} \times \textrm{m}\overline {\textrm{XD}}\)
\(\textrm{m}\overline {\textrm{CX}}\) = \(\textrm{m}\overline {\textrm{XD}}\) = \(\sqrt{\textrm{m}{\overline {\textrm{AX}}} \times \textrm{m}{\overline {\textrm{XB}}}}\)
\(\textrm{m}\overline {\textrm{AB}} \times \textrm{m}\overline {\textrm{CD}}\) + \(\textrm{m}\overline {\textrm{BC}} \times \textrm{m}\overline {\textrm{DS}}\) = \(\textrm{m}\overline {\textrm{CX}} \times \textrm{m}\overline {\textrm{CX}}\)
