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I must confess that I am not able to visualize or understand what is the angle of a spherical triangle say $ABC$ where $A,B,C$ are vertices of the triangle which is formed by intersection of three great circle, and say $a,b,c$ are sides (which are arc on the sphere) of the triangle, what is meant by right spherical triangle say if some one says angle at $C$ is $90$ degree, is it possible to have more than one angle $90$ degree in a spherical triangle I know one result that sum of angles of a spherical triangle is $a+b+c-\pi$, if the radius of the sphere is $r$ then what is the relation between $a,b,c$ with $r$ if there is any. advanced Thank you for clearing my doubts with a picture.

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  • $\begingroup$ A spherical triangle can have three right-angles. $\endgroup$ – A. Chu Mar 17 '13 at 7:50
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    $\begingroup$ Get an orange and slice it into 8 pieces, by cutting in planes through the center. Stare at the pieces. $\endgroup$ – bubba Mar 17 '13 at 8:31
  • $\begingroup$ what about sides?how to define or find their length? $\endgroup$ – miosaki Mar 18 '13 at 4:54
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Here's a picture of a spherical triangle with three right angles. It consists of $1/4$ of the equator and half of two meridians at longitudes $0$ and $\pi/2$.

enter image description here

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