MathDB

5

Part of 2015 Federal Competition For Advanced Students, P2

Problems(1)

Problem 5 -- Making A Point Here

Source: 46th Austrian Mathematical Olympiad National Competition Part 2 Problem 5

7/14/2018
Let I be the incenter of triangle ABCABC and let kk be a circle through the points AA and BB. The circle intersects
* the line AIAI in points AA and PP * the line BIBI in points BB and QQ * the line ACAC in points AA and RR * the line BCBC in points BB and SS
with none of the points A,B,P,Q,RA,B,P,Q,R and SS coinciding and such that RR and SS are interior points of the line segments ACAC and BCBC, respectively.
Prove that the lines PSPS, QRQR, and CICI meet in a single point.
(Stephan Wagner)
geometryincenterAustriaAUT