Geometry Problem. GeoGebra, HTML5 Animation for iPad and Nexus.

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

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## Monday, July 15, 2013

### Problem 902: Triangle, Four Squares, Center, Concurrent Lines

Labels:
concurrent,
square,
triangle

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Connect BJ and EC, which intersect perpendicularly at V; connect BH and AF, which intersect perpendicularly at W (Vecten theorem). Connect VW. Draw circle ACHJ, which passes through V and W (because of right angles at V and W). Connect HM and JM, which are tangents to circle ACHJ. Then cyclic quadrilateral VWHJ with tangents at H and J becomes a 4-point degenerate case of Pascal's hexagon theorem. Thus BM, VH and WJ are concurrent at O. QED

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