Proposed Problem

Click the figure below to see the complete problem 352 about Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

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Complete Problem 352

Level: High School, SAT Prep, College geometry

## Saturday, September 5, 2009

### Problem 352. Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral

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name S circle 1 meet AB, P meet AE, H meet BC

ReplyDeletename J circle 2 meet BC, Y meet ED, V meet DC

ABCD is tangential quadrilateral so =>

AD + BC = AB + DC

AD+MN+FM+NG+BH+JC = AS+BS+DV+CV (HJ = FG, see P355)

AD+MN+FM+NG = AS+DV (BH=BS, JC=CV tang from a point)

AD+MN+FM+NG = AM+MP+DN+NT ( AS=AP=AM+MP,DV=DT=DN+NT)

AD + MN = AM + DN (FM=MP,NG=NT)

second row have to read

ReplyDelete... T meet ED, ...

http://s3.postimg.org/4tcvl07pv/pro_352.png

ReplyDeleteABCD is tangential quadrilateral (see skech)

So AB+CD=BC+AD … (1)

AM=AP-u =AB-x-u

DN=AS-v=CD-y-v

So AM+DN=AB+CD-(x+y)-(u+v)

MN=FG-u-v=QR-u-v=BC-(x+y) -(u+v)

So MN+AD=BC+AD-(x+y)-(u+v)

Replace BC+AD=AB+CD we get AM+DN+MN+AD => quadrilateral AMND is tangential