### Miquel points

If we mark any point on each side of a triangle, and through draw a
circle through the each vertex and the points on the adjacent sides then
the circles will be concurrent at a point called the Miquel point. One special
Miquel point is the point used to form the
pedal triangle.
To observe a GSP sketch that illustrates the position of the Miquel point
for various positions of the points on the sides of the triangle click
here.

There are a number of interesting observations to be made regarding the
Miquel point:

1. The lines from the Miquel points to the marked points on the sides of
the triangle make equal angles with the respective sides. Click
here to observe this property on a GSP sketch.

2.. The centres of the Miquel circles are the vertices of a triangle similar
to the given triangle click here to
observe the similar triangle in a GSP sketch.

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