Talk:Mixtilinear incircles of a triangle

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Maybe add a picture in the introductory paragraph because it is hard to translate the words into a picture.

I don't understand exactly what the following means. Draw the incircle I by intersecting angle bisectors.

I think pictures in every section marking points like ABC D and E for example will be very helpful in following the descriptions.

The information is very good but the math language is a little hard to follow without remembering exactly what the incircle is and other terms so maybe spell out the definition of an incircle and I would draw pictures by hand and label the angles you are referring to.

In the last section you start talking about points D and E without defining them. I know you defined them in an earlier section but I think you should redefine them here. — Preceding unsigned comment added by Zackdu (talk • contribs) 14:11, 25 October 2021 (UTC)

— Preceding unsigned comment added by Zackdu (talk • contribs) 14:04, 25 October 2021 (UTC)

For the first one, thank you for the correction. I meant "incenter". For the other parts, Yes, I am planning to add pictures. This is probably why it is hard to follow. — Preceding unsigned comment added by Tomascr (talk • contribs) 14:09, 25 October 2021 (UTC)

The $$ \sqrt{bc} $$ inversion involves reflection about the angle bisector too. I think you should mention it in the proof that you write using inversion. I like how the headings are not too generic. — Preceding unsigned comment added by Just invert it (talk • contribs) 14:53, 25 October 2021 (UTC)

Mixtilinear excircles
A mixtilinear excircle of a triangle is a circle which is tangent to two lines extending its sides and externally tangent to its circumcircle. The three lines joining a vertex to the point of contact of the circumcircle with the corresponding mixtilinear excircle meet at the internal center of similitude of the incircle and circumcircle. The Online Encyclopedia of Triangle Centers lists this point as X(55).

X(55) is the isogonal conjugate of Gergonne point, and X(56) is the isogonal conjugate of Nagel point. 129.104.241.218 (talk) 00:06, 7 April 2024 (UTC)