MathDB

G4

Part of 2020-IMOC

Problems(1)

IMOC 2020 G4 concyclic wanted, incenter related

Source: https://artofproblemsolving.com/community/c6h2254883p17398793

9/1/2020
Let II be the incenter of triangle ABCABC. Let BIBI and ACAC intersect at EE, and CICI and ABAB intersect at FF. Suppose that RR is another intersection of ⊙(ABC)\odot (ABC) and ⊙(AEF)\odot (AEF). Let MM be the midpoint of BCBC, and P,QP, Q are the intersections of AI,MIAI, MI and EFEF, respectively. Show that A,P,Q,RA, P, Q, R are concyclic.
(ltf0501).
geometryconicsincenter