F.B. page of Erdem Balkan, https://www.facebook.com/photo?fbid=24428580853509491&set=a.949297615197812

 My solution courtesy of Master Alin Pop solution to the nice lemma used for this purpose attached: 

Youtube Channel of Hasan Ata, https://www.youtube.com/watch?v=EYvn10OgqGM&t=29s

 

Geometria Super Top, Anie Luc, 2 Proofs https://www.facebook.com/photo?fbid=122148202394416607&set=gm.2139489633488061&idorvanity=830782544358783

 

Geometria Super Top, Angel Silva Palacios, https://www.facebook.com/photo?fbid=1689125482047636&set=gm.2137937763643248&idorvanity=830782544358783

 

Math.stack.exchange, https://math.stackexchange.com/questions/4769082/angle-cevas-theorem?rq=1

 

https://www.youtube.com/watch?v=EYvn10OgqGM

 

https://math.stackexchange.com/questions/2145456/proving-triangle-dca-is-isosceles-if-point-d-satisfies-angle-dca-angle-d?rq=1

 

https://math.stackexchange.com/questions/4636595/given-a-convex-quadrilateral-abcd-find-the-missing-angle?rq=1

 

, George Tsikaloudakis, https://www.facebook.com/photo/?fbid=122096857881164960&set=pcb.122096858427164960

 

Angel Silva Palacios, Geometria Super Top, https://www.facebook.com/photo?fbid=1683039299322921&set=gm.2131596027610755&idorvanity=830782544358783

 

https://artofproblemsolving.com/community/c4t48f4h3726553_solving_without_using_trigonometry

 

A vanished problem

 

https://artofproblemsolving.com/community/c4t48f4h3725945_geo_problem

 

Math.stackexchange, https://math.stackexchange.com/questions/1128917/prove-that-the-circumcenter-of-triangle-piq-is-on-the-hypotenuse-ac?rq=1

 

Triple angle lemma, general problem of Nelson Tunala, https://www.facebook.com/photo?fbid=25136654412643032&set=a.542610499140765