Seven Problems in Equilateral Triangle
Solution to Problem 3
Given an equilateral triangle $ABC$ with the base extended to twice its length: $AB'=AB.$ Let $B'I$ (with $I$ on $(ABC))$ be the second tangent from $B'$ to the incircle of $\Delta ABC.$
Prove that four points $B',$ $A,$ $O,$ and $I$ are concyclic.
The problem is easily solved by angle chasing.
The proof has been suggested by Machó Bónis at the CutTheKnotMath facebook page.
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