

Online Geometry Problem 154: Triangle, Inradius, Circumradius, Chord.
Level: High School, Honors Geometry, College,
Mathematics Education

In the figure below, ABC is a
triangle inscribed in a circle of center O (circumcenter) and
circumscribed in a circle of center I (incenter). Line BI and
circumcircle meet at D. If r is the inradius and R is the
circumradius, (1) prove that ID = CD, and (2) prove that BI.ID =
2R.r
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