Similar Triangles Determined by Miquel Circles and the Circumcircle
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Let ABC be a triangle and let ,
, and
be points on BC, CA, and AB, respectively. Suppose that the circumcircles of
,
, and
(the Miquel circles) intersect the circumcircle of ABC at points
,
, and
, respectively, where
,
, and
. Let
,
, and
be symmetric to
,
, and
with respect to the midpoints of BC, CA, and AB, respectively. Then
and
are similar.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA