Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
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Tuesday, August 2, 2016
Geometry Problem 1242: Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines
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Let BC and AD extended meet at P
ReplyDeleteThen C2 is the excentre of Tr. PCD
C1 is the in Centre of Tr. PCD
A2 is the in Centre of Tr. PAB
A1 is the excentre of Tr. PAB
It follows that PC1C2A2A1 are collinear points, being on the internal bisector of < P. The concurrency of BC,AD and this line is also self evident
Similarly for AB and DC extended which when extended say meets at Q. Then Q and B1,B2,D1,D2 are collinear and the concurrency of this line and AB and DC is evident
Sumith Peiris
Moratuwa
Sri Lanka