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.
