Saturday, March 9, 2019

Geometry Problem 1423: Triangle, Area, Three Equal Angles, Circumradius, Measurement

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

Details: Click on the figure below.

Geometry Problem 1423: Triangle, Area, Three Equal Angles, Circumradius, Measurement, Tutoring.
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3 comments:

  1. c.t.e.oMarch 9, 2019 at 1:49 PM

    ∆ABC ~ ∆DEF ( ˂B = ˂E, ˂A = ˂D, ˂C = ˂F )
    => S(orange) ~ S(blue)
    => S(∆ABC) = 9.18

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  2. Peter TranMarch 9, 2019 at 6:14 PM

    We have ∠ (EDF)= ∠ (DAB)+ alpha=∠ (BAC)
    ∠ (EFD)= ∠ (FCA)+alpha= ∠ (ACB)
    So triangle DEF similar to ABC ( case AA)
    Ratio of similarity= circum(DEF)/circum(ABC)= .9/2.7= 1/3
    So Area(ABC)= Area(DEF)/(1/9)= 9.18

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  3. Sumith PeirisMarch 10, 2019 at 9:34 PM

    Easily Tr.s ABC & DEF are similar and the ratio of the circumradii = 2.7/0.9 = 3

    So the area of TR. ABC = (1/9)*1.02 = 9.18

    Sumith Peiris
    Moratuwa
    Sri Lanka

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