Thanks to Nibedan Mukherjee who sent me the problem and its solution all the way back in October 2018. I was also told this problem appeared in the 2019 Senior Mathematical Challenge by the UKMT.

2019 Senior Mathematical Challenge paper (see question 25)
https://www.ukmt.org.uk/sites/....default/files/ukmt/s
Solutions (see question 25)
https://www.ukmt.org.uk/sites/....default/files/ukmt/s
Senior Mathematical Challenge archive papers
https://www.ukmt.org.uk/compet....itions/solo/senior-m

The people questioning the names of theorems/rules used in the video should read up on mathematical history. Here are a few references.
Gougu theorem
https://www.rediff.com/news/sp....ecial/did-india-disc
https://www.livemint.com/Opini....on/d3ddePsFMHKZhHLmx
Brahmagupta's formula
https://www-history.mcs.st-and.....ac.uk/HistTopics/Qu
https://en.wikipedia.org/wiki/....Quadratic_equation#H

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