Proposed Problem

Click the figure below to see the complete problem 309.

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Complete Problem 309

Collection of Geometry Problems

Level: High School, SAT Prep, College geometry

## Monday, June 22, 2009

### Problem 309. Regular Nonagon, Diagonals and Side

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Extend AC to J such that CJ = AB=BC=CD etc. Now angle(ACD)=140 -20=120 and thus angle(DCJ)=60. But, CJ==CD so triangle CJD is equilateral with angle(CJD)=60=angle(AED). This makes triangles AED & AJD congruent and therefore, AE=AJ=AC+AB. QED

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ReplyDeleteExtend AB and ED to meet at X. Then Tr.s AEX and BDX are both equilateral and the result follows

ReplyDeleteSumith Peiris

Moratuwa

Sri Lanka

I tried Ptolemy for cyclic quads but failed so far. Anyone can throw light on this?

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