# The Triangles Formed by the Endpoints and Midpoints of Cevians

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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

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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.

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