Geometry Problem 1469: Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration

The figure below shows a triangle ABC with the circumradius R, the inradius r. If \(d, e, f\) are the distances from the midpoints of arcs AB, AC, BC to the sides BC, BC, and AC, respectively, prove that \(d+e+f=2(R+r)\).


Static Diagram of Geometry Problem1469

Dynamic Geometry 1469: Steiner Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration Using GeoGebra, iPad Apps


Poster of the Dynamic Geometry 1469 using iPad Apps

Poster Dynamic Geometry 1469: Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration Using GeoGebra, iPad Apps

Classroom Resource:
Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

  • To explore (show / hide): click/tap a check box.
  • To stop/play the animation: click/tap the icon in the lower left corner.
  • To go to first step: click/tap the "Go to step 1" button.
  • To manipulate the interactive figure: click/tap and drag the blue points or figures.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.

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