Ratios Involving Six Radii

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Given a point on the side
of the triangle
, let
and
be the radii of the inscribed circles of the triangles
and
, and let
and
be the radii of the circumcircles of the triangles
and
. Let
and
denote the radii of the inscribed circle and the circumcircle of the triangle
, respectively. Prove that
.
Contributed by: Jaime Rangel-Mondragon (July 2013)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The label for each radius is placed at the center of the circle of which it is the radius.
This Demonstration comes from problem 8 of the shortlisted problems for the 1970 International Mathematical Olympiad (IMO).
Reference
[1] D. Djukić, V. Janković, I. Matić, and N. Petrović, The IMO Compendium, 2nd ed., New York: Springer, 2011 p. 69.
Permanent Citation
"Ratios Involving Six Radii"
http://demonstrations.wolfram.com/RatiosInvolvingSixRadii/
Wolfram Demonstrations Project
Published: July 11 2013