Question

in $\triangle abc$, the segment $cj = 18$. if $cg = bg$, what is $kj$?

Explanation:

Step1: Recall the centroid property

In a triangle, the centroid divides each median in a ratio of \(2:1\). Here, \(CJ\) is a median (since \(CG = BG\), \(G\) is the mid - point of \(CB\) and \(CJ\) is a line from \(C\) to the mid - point of \(AB\)). Let \(CK = 2x\) and \(KJ=x\), then \(CJ=CK + KJ=3x\).

Step2: Solve for \(x\)

Given \(CJ = 18\), and \(CJ = 3x\). So, \(3x=18\), then \(x=\frac{18}{3}=6\).

Answer:

B. 6