Problem
GEO-B2-M06-P003 Medians
#3
★★☆☆☆ Level 2 of 5
Use Ceva's theorem to prove that the medians of a triangle meet at one point.
Midpoints divide sides in the ratio \(1:1\).
Let \(D,E,F\) be the midpoints of \(BC,CA,AB\). Then \(\frac{BD}{DC}=\frac{CE}{EA}=\frac{AF}{FB}=1\). The product is \(1\), hence by Ceva the medians \(AD\), \(BE\), \(CF\) are concurrent.
A classic first application of Ceva.