Proposed Problem

Click the figure below to see the complete problem 343 about Hexagon, Inscribed Circle, Tangent, Semiperimeter.

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Complete Problem 343

Level: High School, SAT Prep, College geometry

## Thursday, August 20, 2009

### Problem 343. Hexagon, Inscribed Circle, Tangent, Semiperimeter.

Labels:
circle,
circumscribed,
hexagon,
inscribed,
semiperimeter,
tangent

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a hexagon ABCDEF with the inscribed circle O tangent te sides at G,H,M,N,P and K.

ReplyDeletewe have:AG=AK,BG=BH,HC=CM,MD=DN,NE=EP&PF=FK.

s=(AB+BC+CD+DE+EF+FA)/2

s=(AG+GB+BH+HC+CM+MD+DN+NE+EP+PF+FK+KA)/2

s=(AG+BG+BG+CM+CM+MD+MD+EP+EP+PF+PF+AG)/2

s=AG+BG+CM+MD+EP+PF

s=AB+CD+EF

Or:s=BC+DE+AF