Nagel Point
An excircle of a triangle is a circle that is tangent to a side and to lines through the two adjacent sides. A triangle has only one inscribed circle, but it has three excircles.
a) Based on the picture above, how is an excircle constructed?
b) An excircle has been already constructed below. Construct the remaining two excircles of the triangle.
c) The Nagel point is the point of concurrency formed when you draw segments from
the points of tangency to the opposite vertex of the triangle. Construct the Nagel point.
d) Which other points of concurrency is the Nagel point collinear with? (Other points of concurrency have been provided on the diagram: OC = orthocenter, IC = incenter, CT = centroid, CC = circumcenter).