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Results tagged with elementary-proofs
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user 13093
For questions related to 'elementary' proofs in a technical sense, which has nothing to do with the difficulty of the argument or result. A typical example would be 'elementary' proofs of the Prime Number Theorem, which avoid complex analysis. The tag is however not limited to this particular notion of 'elementary.'
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Intersection point of three circles
Switching the roles of $ABC$ and $A'B'C'$, consider the circles passing through the vertices of a triangle $A,B,C$, midpoints of the opposite sides $A',B',C'$ and the circumcenter $O$.
It is straightf …
- 2,222
0
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A generalization of Napoleon's theorem
Notice that triangles $ACD, AEB, FCB$ are similar. Working out the ratios of the sides and the angles one can see that:
Triangles $AI_1I_3$ and $ACE$ are similar. Rotating $I_1I_3$ around $A$ with an …
- 2,222
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Three circles intersecting at one point
It is straightforward to see that $A',B',C'$ are reflections of the circumcenter $O$ with respect to $BC, CA,AB$. Therefore, the center of $(AOA')$ is just the intersection of the mediatrix of $OA$ wi …
- 2,222