Saturday, April 9, 2016

Geometry Problem 1205: Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles

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

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Geometry Problem 1205: Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles
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1 comment:

  1. Pradyumna AgasheApril 10, 2016 at 6:25 AM

    We can use following properties of Napoleon's Equilateral triangles.
    AA'= BB'= CC' And Triangle A1B1C1 is equilateral triangle
    Consider D as midpoint of side AC,
    In Triangle CDC', C1D=C'D/3 And GD=CD/3.Hence line joining C1G is parallel to CC' and also C1G=CC'/3
    Similarly B1G=BB'/3 And A1G=AA'/3
    We get A1G=B1G=C1G, hence G is circumcentre as well as centroid of Triangle A1B1C1 (its equilateral )
    Similarly we can prove for Triangle A2B2C2.

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