The Triangles Formed by the Endpoints and Midpoints of Cevians

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.

Let ABC be a triangle and P be a point. Let AP, BP, and CP intersect BC, AC, and AB or their extensions at A', B', and C', respectively. Let A'', B'', and C'' be the midpoints of AA', BB', and CC'. Let and be the areas of A'B'C' and A''B''C''. Then .

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


Snapshots


Details

Reference

[1] V. Prasolov. Problems in Plane and Solid Geometry, Vol. 1: Plane Geometry (D. Leites, ed. and trans.), Problem 1.35. (Jul 16, 2010) www.students.imsa.edu/~tliu/Math/planegeo.pdf.



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