We are given a triangle with its three medians. In addition to this, we can see that P is the intersection point of the medians, which means that P is the centroid of â–ł XYZ.
By the Centroid Theorem we can write the following equation in relation to XR.
XP = 2/3XR
By the Segment Addition Postulate we get a second equation.
XP + PR = XR
⇒
2/3XR &+ PR = XR
&⇓
PR &= 1/3XR
Finally, let's find XPXR.
XP/PR = 23XR/13XR
⇒
XP/PR = 2 âś“
