Relations

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

[latex]\dfrac{\textrm{m}{\overline {\textrm{AX}}}}{\textrm{m}{\overline {\textrm{CX}}}}[/latex] = [latex]\dfrac{\textrm{m}{\overline {\textrm{DX}}}}{\textrm{m}{\overline {\textrm{BX}}}}[/latex]

relation_metrique_A

[latex]\dfrac{\textrm{m}{\overline {\textrm{AX}}}}{\textrm{m}{\overline {\textrm{XT}}}}[/latex] = [latex]\dfrac{\textrm{m}{\overline {\textrm{XT}}}}{\textrm{m}{\overline {\textrm{BX}}}}[/latex]

[latex]\textrm{m}\overline {\textrm{AX}} \times \textrm{m}\overline {\textrm{XB}}[/latex] = [latex]\textrm{m}\overline {\textrm{CX}} \times \textrm{m}\overline {\textrm{XD}}[/latex]

relation_metrique_D

[latex]\textrm{m}\overline {\textrm{CX}}[/latex] = [latex]\textrm{m}\overline {\textrm{XD}}[/latex] = [latex]\sqrt{\textrm{m}{\overline {\textrm{AX}}} \times \textrm{m}{\overline {\textrm{XB}}}}[/latex]

relation_metrique_C

[latex]\textrm{m}\overline {\textrm{AB}} \times \textrm{m}\overline {\textrm{CD}}[/latex] + [latex]\textrm{m}\overline {\textrm{BC}} \times \textrm{m}\overline {\textrm{DS}}[/latex] = [latex]\textrm{m}\overline {\textrm{CX}} \times \textrm{m}\overline {\textrm{CX}}[/latex]

relation_metrique_B

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