Geometry Problem

Click the figure below to see the complete problem 562.

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Level: High School, SAT Prep, College geometry

## Sunday, January 2, 2011

### Problem 562: Triangle, Cevian, Incenter, Incircle, Perpendicular, Concyclic points, Cyclic Quadrilateral.

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DE, DF bisect the supplementary angles ADB, BDC

ReplyDeleteSo EDF is a right angle

By the result of Problem 561, EGF is a right angle

Hence tha circle on EF as diameter passes through D, G

http://img84.imageshack.us/img84/9576/problem561.png

ReplyDeleteLet I is the midpoint of EF and M is the projection of I over AC

We have angle(EDF)=90 ( see problem 559) and HD=GK (See problem 560)

M is the midpoint of HK . Since HD=GK so M is also the midpoint of DG and triangle DIG is isosceles.

And IE=IF=ID=IG .

Quadrilateral EDGF is cyclic with center of circumcircle at I

Peter Tran