Wednesday, January 15, 2014

Geometry Problem 957: Equilateral Triangle, Inscribed Circle, Incircle, Circumscribed Circle, Circumcircle, Area, Circular Segment

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

Click the figure below to see the complete problem 957.

Online Geometry Problem 957: Equilateral Triangle, Inscribed Circle, Incircle, Circumscribed Circle, Circumcircle, Area, Circular Segment

Posted by Antonio Gutierrez at 9:56 AM
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3 comments:

  1. ion raduJanuary 15, 2014 at 12:15 PM

    (∏R2/3-√3 R2/4)+ (√3 R2/4- ∏R2/12)=∏R2/4

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  2. Ivan BazarovJanuary 15, 2014 at 2:41 PM

    Note that 3*yellow area=OA^2*pi-OF^2*pi=pi(OA^2-(OA/2)^2)=3/4*OA^2*pi, so yellow area=OA^2*pi/4=(OA/2)^2*pi=area of circle with radius OF

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  3. nakaJanuary 15, 2014 at 4:36 PM

    The circumradius is double of the inradius in an equilateral triangle. Thus the blue area is 1/4 of the circumcircle. Since by symmetry, there are 3 equal yellow area, each of them must also be 1/4 of the circumcirlce.

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