In the figure below, ABC is a
triangle inscribed in a circle of center O (circumcenter) and
E is the center (excenter) of the excircle relative to side BC. Line
AE and the circumcircle meet at D. If R is the circumradius and r1
is the exradius (radius of circle E), (1) prove that BD = DE, and (2) prove that
AE.DE = 2R.r1.
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