GERGONNE POINT OF A TRIANGLE.
© 2004-2009. RAIMOND A. STRUBLE, PhD.
DRAFT COPY ONLY.
9/27/2009.
© Raimond A. Struble.
Send comments and correspondence to: Raimond A. Struble,
P. O. Box 50376, Raleigh, NC 27650-6376
and emails to: George.Moore4@va.gov
Problem:
Recognizing that the Gergonne point of a triangle is the point of concurrence
of rays which join the vertices with the points of contact for three mutually
tangent circles centered at the vertices, determine the isosceles triangle
whose Gergonne point falls onto the smallest circle.
FIGURE FOR SUBMITTER'S SOLUTION.
2757.
Proposer's solution: Amazingly, this configuration consists
of the union of two 3×4×5 triangles, where the isosceles
triangle becomes 5×5×8. The proof reduces to four
applications of the cosine law, once the configuration is anticipated.
Last updated: 9/27/2009, by Raimond A. Struble, PhD.