Wednesday, June 5, 2013

Problem 883: Five Tangential or Circumscribed Quadrilaterals, Circle, Tangent, Common Tangent

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 883.

Online Geometry Problem 883: Five Tangential or Circumscribed Quadrilaterals, Circle, Tangent, Common Tangent

1 comment:

  1. http://img29.imageshack.us/img29/2366/problem883.png
    Let b=BR=BZ , a=AY=AX, d=DV=DU and c=CS=CT
    Let b’=B’M’=B’G’ , a’=A’E’=A’N’, d’=D’F’=D’Q’, c’=C’H’=C’P’ ( see attached sketch )
    A’B’C’D’ is a tangential quadrilateral => B’C’+A’D’=A’B’+C’D’
    Add a’+b’+c’+d’ to both sides of above equation and simplify it . we get G’H’+E’F’=M’N’+P’Q’ (1)
    P’Q’ and TU are 2 external tangents to 2 circles so P’Q’=TU
    Similarly E’F’=XV , M’N’=ZY and G’H’=RS
    Replace it in (1) .Equation (1) become RS+XV=ZY+TU
    Add a+b+c+d to both sides of above equation and simplify it . we get BC+AD=BA+CD
    So ABCD is a tangential quadrilateral and AD=BA+CD-BC=2

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