Medians of a Triangle are concurrent and divide each Median in the ratio 2:1

In the given panel below click at any three points O, A and C. Click on the button "Show OAC" to display the triangle OAC. Click on the button "Midpoints P, Q, R" to draw the mid points of the Line O, A and C. You can change the triangle by moving either of the (red) points O, A or C. Click on the button 'Medians' to see that the medians are concurrent, and stay concurrent even when O, A or C are moved. Click at 'Ratio Index' to see that S divides a median in the ratio 2:1. Remember to drag the points O, A or C before changing the 'Ratio Index'.

Reload Applet