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| Circumcenters and Vectors (Posted on 2017-12-31) |
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1) Let I be the incenter of acute ΔABC and A' the circumcenter of ΔIBC.
Prove that A, I, and A' are collinear.
2) Let B' and C' be the circumcenters of triangles ICA and IAB respectively.
Prove that the sum of the vectors IA', IB', and IC' is the zero vector 0
if and only if ΔABC is equilateral.
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Submitted by Bractals
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