Online Geometry Problems

Infographic Geometry Problem 1061: Triangle, Inradius (r), Circumradius (R), Circumcircle, Angle Bisector, Distance from a point to a Line, Perpendicular. Level: High School, SAT Prep, College, Mathematics Education

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In a triangle ABC of inradius r and circumradius R (see the figure below), the bisectors of angles A, B, and C meet the circumcircle O at A1, B1, and C1, respectively. If the distance of A1, B1, and C1 to AC, BC, and AC, respectively, are a1, b1, and c1, respectively, prove that a1 + b1 + c1 = 2.(R + r).
 

Infographic Geometry problem: Triangle, Inradius, Circumradius, Circumcircle, Angle Bisector, Distance from a point to a Line, Perpendicular
 

 



 

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1061-1070 | Triangle | Circumradius | Inradius | Circle | Perpendicular lines | Angle Bisector | Email | Solution / comment | by Antonio Gutierrez
Last updated: Nov 17, 2014