Inner Napoleon Triangle
See complete Problem 247 at:
gogeometry.com/problem/p247_napoleon_theorem_inner_equilateral_triangle.htm
Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Sunday, February 8, 2009
Problem 247. Napoleon's Theorem II. Internal Equilateral triangles
Subscribe to:
Post Comments (Atom)
Create a equilateral triangle AB2B3 ( point B3 is outside triangle ABC) . Connect AB3, AC2, B2B3, B3C2, B2C, CA2
ReplyDelete1. Consider 2 Triangles AB3C2 and ACB. AC2/AB=AB3/AC=1/SQRT(3) and angle B3AC2=angle CAB. these 2 triangles are similar.
2. From (1) we have B3C2=BC/SQRT(3)=CA2
3. 2 triangles B2A2C and B2C2B3 are congruent ( B2C=B2B3, CA2=B3C2, angle A2B2C= angle C2B2B3)
4. So B2A2=B2C2 . Similarly with the same way we get B2C2=C2A2 and triagle A2B2C2 is equilateral.