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

Labels:
angle,
circle,
circumcenter,
circumcircle,
triangle

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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)