The Midpoints of Two Cevians

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

A cevian is a line drawn from a vertex of a triangle to the opposite side.


Let ABC be a triangle and let M and N be the midpoints of the cevians BB' and CC'. Then the area of the quadrilateral BC'B'C is 4 times the area of AMN.


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



The statement of the theorem is in Problem 90. Quadrilateral and Triangle Areas, Midpoints.

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.