The Radii of Four Incircles

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Let ABC be a triangle. Let DEF be parallel to AC with D on AB and E on BC. Let FGH be parallel to AB with G on BC and H on AC. Let ,
,
, and
be the radii of the incircles O,
,
,
of the triangles ABC, DBE, FEG, and CGH, respectively. Then
, with the plus sign when F is outside of ABC and minus when F is inside.
Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA
Snapshots
Details
The statement of the theorem is in Problem 95. Similar Triangles, Inradii, Parallel.
Permanent Citation
"The Radii of Four Incircles"
http://demonstrations.wolfram.com/TheRadiiOfFourIncircles/
Wolfram Demonstrations Project
Published: March 7 2011