Geometry Problem

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

Click the figure below to see the complete problem 699.

## Monday, December 5, 2011

### Problem 699: Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations

Labels:
circle,
circular segment,
equilateral,
inscribed,
metric relations,
midpoint,
triangle

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http://img821.imageshack.us/img821/6871/problem699.png

ReplyDeleteBD cut EF at G ( see picture)

Note that DG=OG (angle ABC=60)

Triangle ABG similar to tri. EDG with ratio =BG/DG=3

So x= AB/3= 4

Peter Tran

DAC = 30, AED = 120 imply ADE = 30

ReplyDeleteSo AE = ED = x

FC = DF = x (by symmetry)

So x = AE = EF = FC = AC/3 = 4