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

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

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## Saturday, April 9, 2016

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

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We can use following properties of Napoleon's Equilateral triangles.

ReplyDeleteAA'= 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.