MathDB

6

Part of India EGMO 2023 TST

Problems(1)

What are those points?

Source: India EGMO TST 2023/6

12/10/2022
Let ABCABC be an isosceles triangle with AB=ACAB = AC. Suppose P,Q,RP,Q,R are points on segments AC,AB,BCAC, AB, BC respectively such that AP=QBAP = QB, ∠PBC=90∘−∠BAC\angle PBC = 90^\circ - \angle BAC and RP=RQRP = RQ. Let O1,O2O_1, O_2 be the circumcenters of △APQ\triangle APQ and △CRP\triangle CRP. Prove that BR=O1O2BR = O_1O_2.
Proposed by Atul Shatavart Nadig
geometryIsosceles Triangleanglechasing