# Using an ellipse, do all inscribed angles have to be congruent?

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?

• The property is bidirectional: congruent angles define a circle. – Yves Daoust Jul 3 '15 at 12:39

## 2 Answers

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).

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?

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