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A constant length $(=a)$ segment of a variable great circle has its extremities $(P,Q)$ moving along fixed Longitudes $(L1,L2)$ passing through North pole $N.$

Please help to identify the geometric parameter with invariant property $\dfrac{\sin a}{\sin A}$ associated with the set of spherical triangles $ NPQ.$

Elusive common Invariant

Narasimham
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  • What exactly are you looking for? Does the sin rules for spherical triangles may help? $\frac{\sin a}{\sin A}=\frac{\sin b}{\sin B}=\frac{\sin c}{\sin C}$ – Alain Remillard Nov 04 '19 at 17:58
  • What geometric object of the spherical triangle set possesses the above property? For flat trigonometry corresponding object is the circum-diameter – Narasimham Nov 05 '19 at 01:11

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