See complete Problem 75
Three Intersecting Circles, Cyclic Quadrilateral, Angles. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, May 19, 2008
Elearn Geometry Problem 75
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What points are M and N?
ReplyDeleteIf N is the point where ED meets AH, why is it on circle 5?
Thank you for your comment:
ReplyDeleteLine AH and circle 3 meet at M, Line DE and circle 5 meet at N.
The graphic was updated.
Thank you.
ang EAH = ang EBM ( AEHD cyclic, arc EFM )
ReplyDeleteang EDH = ang NCH ( NCDH cyclic. arc HGN
EAH = EAD ( from P 73, AEHD cyclic )
=>
EBM = NCH
=>
PBQ = PCQ ( as vertikal angles )
from
geometry help P39, 16.2
PBCQ cyclic
Join DH and by the result of problem 74, BCQP is a cyclic quad (converse of < in same seg.)
ReplyDelete