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For circles, it is well known that all inscribed angles are congruent. With the definition of inscribed angles maintained to ellipses, are all inscribed angles of an ellipse congruent?

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  • $\begingroup$ The property is bidirectional: congruent angles define a circle. $\endgroup$ – Yves Daoust Jul 3 '15 at 12:39
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HINT: Let us imagine an ellipse, where major axis is very large with comparison to minor axis. Consider two triangles: the first with two equal and the second with two very different edges (the third is major axis).

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If you apply special cases of generally established results it is ok. You cannot always generalize results of particular situations that easily, without including all features correctly together.

In a circle there is a single center. In an ellipse there are two centers, the foci. So then how can you generalize?

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  • $\begingroup$ @Narasimhan: There are the foci, and then there is the center. $\endgroup$ – Orest Bucicovschi Jul 2 '15 at 23:18
  • $\begingroup$ @Orangeskid OK,how is single center of circle split into two foci and their mid-point? $\endgroup$ – Narasimham Jul 3 '15 at 9:14

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