Projections, an Altitude, and the Orthocenter

Requires a Wolfram Notebook System

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

The intersection of the altitudes of a triangle is the orthocenter.

[more]

The product of the projections of two sides of a triangle onto the third side is equal to the product of the altitude to that side and the distance of the orthocenter to that side.

In terms of the figure, let H be the orthocenter of the triangle ABC and let B' be the intersection of BH and AC. Then the projections of AB and BC onto AC are AB' and B'C, the altitude is BB', and the distance from the orthocenter to AC is HB'. Then AB'×B'C = BB'×HB'.

[less]

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details



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