Three Equal Segments from the Altitudes of a Triangle

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

In the triangle let the feet of the altitudes be , , and . The circle with diameter meets and at two points other than to form a segment of length ; similarly define and . Prove that .

Contributed by: Jaime Rangel-Mondragon (July 2013)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The segments of equal length are drawn in blue.

This Demonstration comes from problem 19 of the shortlisted problems for the 1971 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. 73.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send