# Online Geometry Problem 909: Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Incenter, Inradius, Distance. Level: High School, College, Mathematics Education

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 In a bicentric quadrilateral ABCD, I is the incenter , O the circumcenter, and r the inradius, If AI = a, BI = b, CI =c, and DI = d, prove that . A bicentric quadrilateral ABCD is a convex quadrilateral that has both an incircle I and a circumcircle O.     Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
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