Given a reference triangle △ABC, a reflection triangle △A′B′C′ is generated by reflecting each vertex about the opposite side, for example A′ is generated by reflecting vertex A about side BC. Now, suppose the vertices A′, B′ and C′ are given, how can you find the original vertices of the original triangle △ABC?

(In reply to

What am I missing? by Steve Herman)

There is a joke something to the effect that from three numbers a good statistician can generate 22 statistical measures.

Likewise, from following this site for a while, I have learned of the many very different centers one triangle can have (via definition of "center").

Likewise, I just now understand _what_ a reflection triangle is (see, e.g. wikipedia and Wolfram Alpha) and have learned that reversing the reflection is not pretty.

Multiple triangle centers and reversing a reflection come together in this

**paper,** which, in order to answer this problem, I would have to first understand. I am hoping someone will beat me to it.

*Edited on ***July 15, 2020, 4:14 pm**