THEOREM OF THE DAY: Miquel’s Triangle Theorem

Theorem

Let $A,B$ and $C$ be the vertices of a triangle and $a,b$ and $c$ be points chosen on sides $CB,AC$ and $AB$, respectively. 

Then the circles defined by $bAc,cBa$ and $aCb$ have a common point of intersection. Moreover, if $a,b$ and $c$ are chosen to be collinear then this point lies on the circle defined by $A,B$ and $C$.

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