Geometry Problem. Post your solution in the comment box below.

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

Details: Click on the figure below.

## Saturday, March 9, 2019

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

Labels:
angle,
area,
circumradius,
geometry problem,
measurement,
triangle

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∆ABC ~ ∆DEF ( ˂B = ˂E, ˂A = ˂D, ˂C = ˂F )

ReplyDelete=> S(orange) ~ S(blue)

=> S(∆ABC) = 9.18

We have ∠ (EDF)= ∠ (DAB)+ alpha=∠ (BAC)

ReplyDelete∠ (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

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

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

Sumith Peiris

Moratuwa

Sri Lanka