Thursday, July 24, 2014

Geometry Problem 1033: Triangle, Angle Obtuse, Circumcircle, Diameter, Area

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 1033.

Online Math: Geometry Problem 1033: Triangle, Angle Obtuse, Circumcircle, Diameter, Area

Posted by Antonio Gutierrez at 2:33 PM
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2 comments:

  1. Jacob HA (EMK2000)July 24, 2014 at 4:47 PM

    Let S(ABC) be the area of ABC.

    S(CDE) = S(ABF) = 2
    S(ACDE) = 11+2 = 13
    S(OCDE) = 13/2
    S(OCE) = 13/2 - 2 = 9/2
    S(BCE) = 9

    S(AEF) = S(BCD) = 4
    S(ACEF) = 11+4 = 15
    S(AOEF) = 15/2
    S(AOE) = 15/2 - 4 = 7/2
    S(ABE) = 7

    S(ABC) = 9+7-11 = 5

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  2. Ivan BazarovJuly 30, 2014 at 9:39 AM

    AC=FD, CE=BF, and AE=BD, so [BFD]=[ECA]=11.
    [ABC]=2+4+11-[ACDF]=2+4+11-2[ACF]=2+4+11-2(2+4)=5

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