A Relation between Incircles and Excircles

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Let ABC be a triangle and M be a point on BC. Let ,
, and
be the radii of the incircles of the triangles ACM, ABM, and ABC and let
,
, and
be the radii of the corresponding excircles tangent to BC. Then
.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
This is problem 1 from the 12-th International Mathematical Olympiad.
Permanent Citation
"A Relation between Incircles and Excircles"
http://demonstrations.wolfram.com/ARelationBetweenIncirclesAndExcircles/
Wolfram Demonstrations Project
Published: March 7 2011