Geometry Problem
Click the figure below to see the complete problem 476 about Triangle, Circumcenter, Circumcircle, Angles.
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Complete Problem 476
Level: High School, SAT Prep, College geometry
Sunday, July 18, 2010
Problem 476: Triangle, Circumcenter, Circumcircle, Angles
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Let circle H intersect circle M at N.
ReplyDeleteLet (ABC) denote angle (ABC)
1. We have (ENF)= (ABC) [Both angles supplement to Angle EBF]
(END) =(BAC) [Both angles supplement to Angle EAD]
2. (DNF)= (ENF)+(END)=(ABC)+(BAC) so (DNF) supplement to angle (C )
3. So quadrilateral CDNF is cyclic.
4. EN is the common secant of circle H and circle M so HM perpendicular to EN
DN is the common secant of circle H and circle G so HG perpendicular To DN
5. So (MHG)=(END)=(BAC)