Introducing "3 circumcenter method"

[PDF] Completion of finding proofs for generalized Langley's problems in elementary geometry (DRAFT/20180609)

translated from "初等幾何で整角四角形を完全制覇", 現代数学2016.2, pp.66-73
Hiroshi Saito (斉藤 浩)

On October 27th, 2015, a proof for a problem which had been unproven in elementary geometry until then was presented by Ms. aerile_re on the internet. The method she used, named "3 circumcenter method", can be applied to every generalized Langley's problems, and that was the answer for the longstanding problem left by J. F. Rigby in 1978. I was honored to introduce her method on a magazine "現代数学" ("Gendai Suugaku" means "modern mathematics"), and I thought this discovery should be known in all over the world. So I decided to translate the article into English. Here, the translation is released as a draft, because there may be some mistranslation and this is still under correcting errors.

Dedicated to Dr. John Frankland Rigby (Apr.22nd 1933 - Dec.29th 2014).