MathDB

2.2

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 2.2 concurrency

Source:

6/6/2020
Let ABCABC be a scalene triangle. A circle (O)(O) passes through B,CB,C, intersecting the line segments BA,CABA,CA at F,EF,E respectively. The circumcircle of triangle ABEABE meets the line CFCF at two points M,NM,N such that MM is between CC and FF. The circumcircle of triangle ACFACF meets the line BEBE at two points P,QP,Q such that PP is betweeen BB and EE. The line through NN perpendicular to ANAN meets BEBE at RR, the line through QQ perpendicular to AQAQ meets CFCF at SS. Let UU be the intersection of SPSP and NR,VNR, V be the intersection of RMRM and QSQS. Prove that three lines NQ,UVNQ,UV and RSRS are concurrent.
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concurrentgeometrycircumcirclecircles