IMO 2022 - International Mathematical Olympiad | GEOMETRY | PROBLEM 4

A solution to problem No. 4 (Geometry) of the 63rd International Mathematical Olympiad held in Oslo - Norway is proposed.
Properties used:
Triangular congruence.
Triangular similarity.
Measure of the external angle as the sum of two measures of internal angles in a triangle.
Internal and external angles in quadrilaterals.
Point power (Secanting chords theorem).
Inscribable quadrilaterals.
As a curious fact (or maybe not), the 6 students of the Republic of China obtained the perfect score (42 points), this team was made up of:
Xiaoyu Qu
7 7 7 7 7 7 42 1 100.00% Gold medal
Jiayu Liu
7 7 7 7 7 7 42 1 100.00% Gold medal
Yubo Liao
7 7 7 7 7 7 42 1 100.00% Gold medal
Zhicheng Zhang
7 7 7 7 7 7 42 1 100.00% Gold medal
Yiran Zhang
7 7 7 7 7 7 42 1 100.00% Gold medal
Cheng Jiang
7 7 7 7 7 7 42 1 100.00% Gold medal
Special mention deserves the Peruvian team, which managed to place itself in position No. 19 in the global table, and first place in relation to Latin American countries, with the same accumulated as Brazil.
The students of the Peruvian team were:
Diego Coronado
7 7 2 7 7 3 33 45 92.52% Silver medal
Yohan Min
7 7 2 7 7 1 31 68 88.61% Silver medal
Carla Fermin
7 7 1 7 7 2 31 68 88.61% Silver medal
FLOR LUNA
7 7 2 7 4 0 27 187 68.37% Bronze medal
Joaquin Guerra
6 7 1 7 6 0 27 187 68.37% Bronze medal
Eduardo Aragon
7 0 2 7 7 1 24 247 58.16% Bronze medal
Head of the delegation: Jesus Zapata
Tutor: Jorge Tipe.

[@lopezhernandezalexdaniel2727]

Muy buenas explicaciones, más de estos vídeos. Inunda TH-cam con estos vídeos tan educativos. Todo mi apoyo.

[@edwardjorgeterres4351]

Me agrada tu canal no te rindas. Exitos

[@marcoantonioaronegrajeda5628]

Excelente solución Maestro...

[@edwardjorgeterres4351]

Felicidades. Siga maestro.

[@OlympicMaths]

Saludos @edwardjorgeterres4351

[@matematicasconprofedenis1921]

Excelente DR

[@martinperu6207]

Con libro comienzo para tener base teórica y poder enfrentar estos problemas..

[@anthonymatute5888]

colegio saco oliveros y prolog excelente semilleros y tambien olvidarme acadmia cesar vallejo y bertolt brecht saludos

[@OlympicMaths]

Genial. Claro que sí.

[@MariaPerez-ul9dp]

Cuando llegaste en el minuto 8:56, ya simplemente podrías haber terminado de una forma más sencilla, el ángulo PRS=angPDS-angDSR y angPQS=angCQS-angCQP
pero PDS=CQS y DSR=CQP por tanto PRS=PQS y ya ahi se demuestra a él cuadrilátero PEQS es cíclico