Sunday, August 4, 2013

Problem 907: Bicentric Quadrilateral, Incircle, Circumcircle, Circunscribed, Inscribed, Tangent, Inradius

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

Click the figure below to see the complete problem 907.

Online Geometry Problem 907: Bicentric Quadrilateral, Incircle, Circumcircle, Circunscribed, Inscribed, Tangent, Inradius.

Posted by Antonio Gutierrez at 9:17 AM
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2 comments:

  1. UnknownAugust 4, 2013 at 3:28 PM

    build CI IG and AI
    BAH=2a=>C=180-2a
    IAH=a, ICG=90-a
    CGI=IHA=90=>CIG=a=IAH
    =>CIG~IAH
    1/x=x/3=>x=sqrt(3)

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  2. Peter TranAugust 4, 2013 at 4:44 PM

    Minor correction due to typo error.

    In right triangle IHA we have IH=x= 3*tan(A/2)
    in right triangle IGC we have x= CG*tan(C/2)= 1/tan(A/2) ...(A supplement to C)
    Replace it in 1st expression we have x=3(1/x) => x=SQRT(3)

    Peter Tran

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