Geometry Problems, Online Education

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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Triangle, inradius, circumradius

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