Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.

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## Saturday, June 11, 2016

### Geometry Problem 1227: Triangle, Circumcircle, Angle Bisector, Concyclic Points, Cyclic Quadrilateral

Labels:
angle bisector,
circle,
circumcircle,
concyclic,
cyclic quadrilateral,
triangle

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Problem 1227

ReplyDeleteIs <PAE=x=<EAD=<FBD=<PBE,then A,B,E,P are concyclic so <ABD=<DFE=<AFR,and <ABE=<EPC=<APR,but <ABE=<EPC=<APR therefore A,F,P,R are concyclic.

Is <RAP=y=<RFP=<BFD=<BAD,but <RAD=2x+y=<PAB=<PEC=<REC therefore A,D,E,R are concyclic.

APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE