Problem 6.
Let

be an equilateral triangle. Let

be interior points of

such that
,
,
, and

Let

and

meet at

let

and

meet at

and let

and

meet at

Prove that if triangle

is scalene, then the three circumcircles of triangles

and

all pass through two common points.
(Note: a scalene triangle is one where no two sides have equal length.)
proposed by
Ankan Bhattacharya , USA